## Trigonometry Study Materials PDF With Practice Questions Worksheet

## Trigonometry Study Materials PDF For Competitive Exams

## Six Important Trigonometric Functions

## Trigonometry Ratios Table

## Trigonometry Formula

## 1. Pythagorean Identities

- sin ² θ + cos ² θ = 1
- tan 2 θ + 1 = sec 2 θ
- cot 2 θ + 1 = cosec 2 θ
- sin 2θ = 2 sin θ cos θ
- cos 2θ = cos² θ – sin² θ
- tan 2θ = 2 tan θ / (1 – tan² θ)
- cot 2θ = (cot² θ – 1) / 2 cot θ

## 2. Sum and Difference identities-

For angles A and B, we have the following relationships:

- sin(A + B) = sin(A)cos(B) + cos(A)sin(B)
- cos(A + B) = cos(A)cos(B) – sin(A)sin(B)
- tan(A + B) = tan(A) + tan(B)/1−tan(A) tan(B)
- sin(A – B) = sin(A)cos(B) – cos(A)sin(B)
- cos(A – B) = cos(A)cos(B) + sin(u)sin(v)
- tan(A – B) = tan(A) − tan(B)/1+tan(A) tan(B)

## 3. If A, B and C are angles and a, b and c are the sides of a triangle, then,

## Trigonometry Questions & Answers For Competitive Exams

Question 1: In a ΔABC right angled at B if AB = 12, and BC = 5 find sin A and tan A, cos C and cot C

AC=√((AB)^2+(BC)^2 ) =√(〖12〗^2+5^2 ) =√(144+25) =√169=13

When we consider t-ratios of ∠C, we have Base = BC = 5 Perpendicular = AB = 12 Hypotenuse = AC = 13

cosC = Base/Hypotenuse = 5/13 cotC = Base/Perpendicular = 5/12

Question 2 : Find the value of 2 sin2 30° tan 60° – 3 cos2 60° sec2 30°

Solution: 2(1/2)^2×√3-3(1/2)^2×(2/√3)^2 =2×1/4×√3-3×1/4×4/3=√3/2-1=(√3-2)/2

Question 3 : In a right triangle ABC right angle at B the six trigonometric ratios of ∠C

Solution: sinA=Perpendicular/Hypotenuse=3/5

Base=√((Hypotenuse)^2-(Perpendicualr)^2 ) =√(5^2-3^2 ) =√(25-9)=√16=4

Now sinC=BC/AC=4/5,cosecC=5/4 cosC=3/5=AB/AC,secC=5/3 tanC=AB/AC=4/3,cotC=3/4

Question 4 : Find the value of 2 sin2 30° tan 60° – 3 cos2 60° sec2 30°

Question 5 : bFind the value θ sin2θ=√3

Solution: sin2θ= √3/2 2θ = 60 θ = 30°

Question 6 : Find the value of x. Tan 3x = sin 45° cos 45° + sin 30°

Solution: tan3x=1/√2×1/√2+1/2 =1/2+1/2=1 ⇒tan3x=1 ⇒ tan3x = tan45° 3x = 45° X = 15°

## Trigonometry Problems & Solutions

Q.1: In △ABC, right-angled at B, AB=22cm and BC=17cm. Find:

Q.2: If 12cot θ= 15, then find sec θ?

Q.4: If sec 4θ = cosec (θ- 300), where 4θ is an acute angle, find the value of A.

## Height And Distance

Though we cannot measure them easily, we can determine these by using trigonometric ratios.

## Line of Sight

Sol: Let the height of the wall be h.

## Trigonometry Practice Questions Worksheet PDF

## Trigonometry Frequently Asked Questions

## 9 thoughts on “Trigonometry Study Materials PDF With Practice Questions Worksheet”

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## Trigonometry Worksheets for High School

## List of Trigonometry Worksheets

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Conversion of Degrees and Radians

Trigonometric Ratios | Right Triangle Trigonometry

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## Unit: Trigonometry

- Unit circle (Opens a modal)
- The trig functions & right triangle trig ratios (Opens a modal)
- Trig unit circle review (Opens a modal)
- Unit circle Get 3 of 4 questions to level up!
- Intro to radians (Opens a modal)
- Radians & degrees (Opens a modal)
- Degrees to radians (Opens a modal)
- Radians to degrees (Opens a modal)
- Radian angles & quadrants (Opens a modal)
- Radians & degrees Get 3 of 4 questions to level up!
- Unit circle (with radians) Get 3 of 4 questions to level up!

## The Pythagorean identity

- Proof of the Pythagorean trig identity (Opens a modal)
- Using the Pythagorean trig identity (Opens a modal)
- Pythagorean identity review (Opens a modal)
- Use the Pythagorean identity Get 3 of 4 questions to level up!

## Trigonometric values of special angles

## Graphs of sin(x), cos(x), and tan(x)

- Graph of y=sin(x) (Opens a modal)
- Intersection points of y=sin(x) and y=cos(x) (Opens a modal)
- Graph of y=tan(x) (Opens a modal)

## Amplitude, midline and period

- Features of sinusoidal functions (Opens a modal)
- Midline, amplitude, and period review (Opens a modal)
- Midline of sinusoidal functions from graph Get 3 of 4 questions to level up!
- Amplitude of sinusoidal functions from graph Get 3 of 4 questions to level up!
- Period of sinusoidal functions from graph Get 3 of 4 questions to level up!

## Transforming sinusoidal graphs

- Amplitude & period of sinusoidal functions from equation (Opens a modal)
- Transforming sinusoidal graphs: vertical stretch & horizontal reflection (Opens a modal)
- Transforming sinusoidal graphs: vertical & horizontal stretches (Opens a modal)
- Amplitude of sinusoidal functions from equation Get 3 of 4 questions to level up!
- Midline of sinusoidal functions from equation Get 3 of 4 questions to level up!
- Period of sinusoidal functions from equation Get 3 of 4 questions to level up!

## Graphing sinusoidal functions

- Example: Graphing y=3⋅sin(½⋅x)-2 (Opens a modal)
- Example: Graphing y=-cos(π⋅x)+1.5 (Opens a modal)
- Sinusoidal function from graph (Opens a modal)
- Graph sinusoidal functions Get 3 of 4 questions to level up!
- Construct sinusoidal functions Get 3 of 4 questions to level up!
- Graph sinusoidal functions: phase shift Get 3 of 4 questions to level up!

## Sinusoidal models

- Interpreting trigonometric graphs in context (Opens a modal)
- Trig word problem: modeling daily temperature (Opens a modal)
- Trig word problem: modeling annual temperature (Opens a modal)
- Trig word problem: length of day (phase shift) (Opens a modal)
- Trigonometry: FAQ (Opens a modal)
- Interpreting trigonometric graphs in context Get 3 of 4 questions to level up!
- Modeling with sinusoidal functions Get 3 of 4 questions to level up!
- Modeling with sinusoidal functions: phase shift Get 3 of 4 questions to level up!

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## 1000+ Trigonometry PDF (Questions & Solution with Shortcut Tricks) – Download Now

Trigonometry pdf questions & solution with shortcut tricks.

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## 3.3: Solving Trigonometric Equations

- Use the fundamental identities to solve trigonometric equations.
- Express trigonometric expressions in simplest form.
- Solve trigonometric equations by factoring.
- Solve trigonometric equations by using the Quadratic Formula.

## Solving Linear Trigonometric Equations in Sine and Cosine

\[\sin \theta=\sin(\theta \pm 2k\pi)\]

Example \(\PageIndex{1A}\): Solving a Linear Trigonometric Equation Involving the Cosine Function

Find all possible exact solutions for the equation \(\cos \theta=\dfrac{1}{2}\).

From the unit circle, we know that

These are the solutions in the interval \([ 0,2\pi ]\). All possible solutions are given by

Example \(\PageIndex{1B}\): Solving a Linear Equation Involving the Sine Function

Find all possible exact solutions for the equation \(\sin t=\dfrac{1}{2}\).

\[t=\dfrac{\pi}{6}\pm 2\pi k \quad \text{and} \quad t=\dfrac{5\pi}{6}\pm 2\pi k \nonumber\]

How to: Given a trigonometric equation, solve using algebra

- Look for a pattern that suggests an algebraic property, such as the difference of squares or a factoring opportunity.
- Substitute the trigonometric expression with a single variable, such as \(x\) or \(u\).
- Solve the equation the same way an algebraic equation would be solved.
- Substitute the trigonometric expression back in for the variable in the resulting expressions.
- Solve for the angle.

Example \(\PageIndex{2}\): Solve the Linear Trigonometric Equation

Solve the equation exactly: \(2 \cos \theta−3=−5\), \(0≤\theta<2\pi\).

Use algebraic techniques to solve the equation.

Solve exactly the following linear equation on the interval \([0,2\pi)\): \(2 \sin x+1=0\).

\(x=\dfrac{7\pi}{6},\space \dfrac{11\pi}{6}\)

## Solving Equations Involving a Single Trigonometric Function

Example \(\PageIndex{3A}\): Solving a Trignometric Equation Involving Sine

Solve the problem exactly: \(2 {\sin}^2 \theta−1=0\), \(0≤\theta<2\pi\).

Example \(\PageIndex{3B}\): Solving a Trigonometric Equation Involving Cosecant

Solve the following equation exactly: \(\csc \theta=−2\), \(0≤\theta<4\pi\).

We want all values of \(\theta\) for which \(\csc \theta=−2\) over the interval \(0≤\theta<4\pi\).

Example \(\PageIndex{3C}\): Solving an Equation Involving Tangent

Solve the equation exactly: \(\tan\left(\theta−\dfrac{\pi}{2}\right)=1\), \(0≤\theta<2\pi\).

Over the interval \([ 0,2\pi )\),we have two solutions:

\(\theta=\dfrac{3\pi}{4}\) and \(\theta=\dfrac{3\pi}{4}+\pi=\dfrac{7\pi}{4}\)

Find all solutions for \(\tan x=\sqrt{3}\).

Example \(\PageIndex{4}\): Identify all Solutions to the Equation Involving Tangent

Identify all exact solutions to the equation \(2(\tan x+3)=5+\tan x\), \(0≤x<2\pi\).

## Solve Trigonometric Equations Using a Calculator

Example \(\PageIndex{5A}\): Using a Calculator to Solve a Trigonometric Equation Involving Sine

Use a calculator to solve the equation \(\sin \theta=0.8\),where \(\theta\) is in radians.

The angle measurement in degrees is

Example \(\PageIndex{5B}\): Using a Calculator to Solve a Trigonometric Equation Involving Secant

Use a calculator to solve the equation \( \sec θ=−4, \) giving your answer in radians.

We can begin with some algebra.

Check that the MODE is in radians. Now use the inverse cosine function

The solutions are \(\theta≈1.8235\pm 2\pi k\) and \(\theta≈4.4597\pm 2\pi k\).

\(\theta≈1.7722\pm 2\pi k\) and \(\theta≈4.5110\pm 2\pi k\)

## Solving Trigonometric Equations in Quadratic Form

Example \(\PageIndex{6A}\): Solving a Trigonometric Equation in Quadratic Form

Solve the equation exactly: \({\cos}^2 \theta+3 \cos \theta−1=0\), \(0≤\theta<2\pi\).

Replace \(x\) with \(\cos \theta \) and solve.

Example \(\PageIndex{6B}\): Solving a Trigonometric Equation in Quadratic Form by Factoring

Solve the equation exactly: \(2 {\sin}^2 \theta−5 \sin \theta+3=0\), \(0≤\theta≤2\pi\).

Make sure to check all solutions on the given domain as some factors have no solution.

\(\cos \theta=−1\), \(\theta=\pi\)

Example \(\PageIndex{7A}\): Solving a Trigonometric Equation Using Algebra

Solve exactly: \(2 {\sin}^2 \theta+\sin \theta=0;\space 0≤\theta<2\pi\)

Example \(\PageIndex{7B}\): Solving a Trigonometric Equation Quadratic in Form

We can factor using grouping. Solution values of \(\theta\) can be found on the unit circle.

Solve the quadratic equation \(2{\cos}^2 \theta+\cos \theta=0\).

\(\dfrac{\pi}{2}, \space \dfrac{2\pi}{3}, \space \dfrac{4\pi}{3}, \space \dfrac{3\pi}{2}\)

## Solving Trigonometric Equations Using Fundamental Identities

Example \(\PageIndex{8}\): Solving an Equation Using an Identity

If we rewrite the right side, we can write the equation in terms of cosine:

Our solutions are \(\theta=\dfrac{2\pi}{3},\space \dfrac{4\pi}{3},\space \pi\).

## Solving Trigonometric Equations with Multiple Angles

Example \(\PageIndex{9}\): Solving a Multiple Angle Trigonometric Equation

Solve exactly: \(\cos(2x)=\dfrac{1}{2}\) on \([ 0,2\pi )\).

Are there any other possible answers? Let us return to our first step.

## Key Concepts

- When solving linear trigonometric equations, we can use algebraic techniques just as we do solving algebraic equations. Look for patterns, like the difference of squares, quadratic form, or an expression that lends itself well to substitution. See Example \(\PageIndex{1}\), Example \(\PageIndex{2}\), and Example \(\PageIndex{3}\).
- Equations involving a single trigonometric function can be solved or verified using the unit circle. See Example \(\PageIndex{4}\), Example \(\PageIndex{5}\), and Example \(\PageIndex{6}\), and Example \(\PageIndex{7}\).
- We can also solve trigonometric equations using a graphing calculator. See Example \(\PageIndex{8}\) and Example \(\PageIndex{9}\).
- Many equations appear quadratic in form. We can use substitution to make the equation appear simpler, and then use the same techniques we use solving an algebraic quadratic: factoring, the quadratic formula, etc. See Example \(\PageIndex{10}\), Example \(\PageIndex{11}\), Example \(\PageIndex{12}\), and Example \(\PageIndex{13}\).
- We can also use the identities to solve trigonometric equation. See Example \(\PageIndex{14}\), Example \(\PageIndex{15}\), and Example \(\PageIndex{16}\).
- We can use substitution to solve a multiple-angle trigonometric equation, which is a compression of a standard trigonometric function. We will need to take the compression into account and verify that we have found all solutions on the given interval. See Example \(\PageIndex{17}\).
- Real-world scenarios can be modeled and solved using the Pythagorean Theorem and trigonometric functions. See Example \(\PageIndex{18}\).

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## 600+ Trigonometry Question with Solution Free PDF – Download Free

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## Trigonometry Review and Practice Questions

## Quick Review with Examples

There are 2 more important trigonometric functions, tangent and cotangent:

If a is 9 cm and c is 18 cm, find α.

We can use the sine for this problem:

We can see from the table that if sinα is 1/2, then angle α is 30⁰.

## Practice Questions

1. If sides a and b of a right triangle are 8 and 6, respectively, find cosine of α.

2. Find tangent of a right triangle, if a is 3 and c is 5.

3. If α=30 0 , find sin30 0 + cos60 0 .

4. Calculate (sin 2 30 0 – sin0 0 )/(cos90 0 – cos60 0 ).

5. Find cotangent of a right angle.

## Answer Key

a = 8 b = 6 a 2 + b 2 = c 2 8 2 + 6 2 = c 2 64 + 36 = c 2 c 2 = 100 c = 10 cosα = b/c = 6/10 = 3/5

2. D 3/4 a = 3 c = 5 a 2 + b 2 = c 2 3 2 + b 2 = 5 2 b 2 = 25 – 9 b 2 = 16 b = 4 tgα = a/b = 3/4

3. C 1 α = 30 0 sin30 0 + cos60 0 = 1/2 + 1/2 = 1

(sin 2 30 0 – sin0 0 ) / (cos90 0 – cos60 0 ) = ((1/2) 2 – 0) / (0 – 1/2) = (1/4) / (-1/2) = -1/2

α = 90 0 ctg90 0 = cos90 0 / sin90 0 = 0/1 = 0

## Antonym Practice Questions and Tutorials

Logarithms review and practice questions, you may also like.

## Inverse Functions Practice Questions

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Nice questions will u plz add some more interesting questions from trigonometry

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## Trigonometry Questions

The basic trigonometric ratios are defined as follows.

sine of ∠A = sin A = Side opposite to ∠A/ Hypotenuse

cosine of ∠A = cos A = Side adjacent to ∠A/ Hypotenuse

tangent of ∠A = tan A = (Side opposite to ∠A)/ (Side adjacent to ∠A)

cosecant of ∠A = cosec A = 1/sin A = Hypotenuse/ Side opposite to ∠A

secant of ∠A = sec A = 1/cos A = Hypotenuse/ Side adjacent to ∠A

cotangent of ∠A = cot A = 1/tan A = (Side adjacent to ∠A)/ (Side opposite to ∠A)

## Trigonometry Questions and Answers

1. From the given figure, find tan P – cot R.

In the right triangle PQR, Q is right angle.

So, tan P – cot R = (5/12) – (5/12) = 0

2. Prove that (sin 4 θ – cos 4 θ +1) cosec 2 θ = 2

L.H.S. = (sin 4 θ – cos 4 θ +1) cosec 2 θ

= [(sin 2 θ – cos 2 θ) (sin 2 θ + cos 2 θ) + 1] cosec 2 θ

Using the identity sin 2 A + cos 2 A = 1,

= (sin 2 θ – cos 2 θ + 1) cosec 2 θ

= [sin 2 θ – (1 – sin 2 θ) + 1] cosec 2 θ

3. Prove that (√3 + 1) (3 – cot 30°) = tan 3 60° – 2 sin 60°.

Therefore, (√3 + 1) (3 – cot 30°) = tan 3 60° – 2 sin 60°.

4. If tan(A + B) = √3 and tan(A – B) = 1/√3 ; 0° < A + B ≤ 90°; A > B, find A and B.

Therefore, A = 45° and B = 15°.

5. If sin 3A = cos (A – 26°), where 3A is an acute angle, find the value of A.

sin 3A = cos(A – 26°); 3A is an acute angle

cos(90° – 3A) = cos(A – 26°) {since cos(90° – A) = sin A}

6. If A, B and C are interior angles of a triangle ABC, show that sin (B + C/2) = cos A/2.

Dividing both sides of this equation by 2, we get;

sin (B + C)/2 = sin (90° – A/2)

⇒ sin (B + C)/2 = cos A/2 {since sin(90° – x) = cos x}

7. If tan θ + sec θ = l, prove that sec θ = (l 2 + 1)/2l.

(sec θ – tan θ)(sec θ + tan θ) = 1

(sec θ – tan θ) l = 1 {from (i)}

tan θ + sec θ + sec θ – tan θ = l + (1/l)

LHS = (cos A – sin A + 1)/ (cos A + sin A – 1)

Dividing the numerator and denominator by sin A, we get;

= (cot A – 1 + cosec A)/(cot A + 1 – cosec A)

Using the identity cosec 2 A = 1 + cot 2 A ⇒ cosec 2 A – cot 2 A = 1,

= [cot A – (cosec 2 A – cot 2 A) + cosec A]/ (cot A + 1 – cosec A)

= [(cosec A + cot A) – (cosec A – cot A)(cosec A + cot A)] / (cot A + 1 – cosec A)

9. Prove that: (cosec A – sin A)(sec A – cos A) = 1/(tan A + cot A)

[Hint: Simplify LHS and RHS separately]

LHS = (cosec A – sin A)(sec A – cos A)

= (cos 2 A/sin A) (sin 2 A/cos A)

= (sin A cos A)/ (sin 2 A + cos 2 A)

i.e. (cosec A – sin A)(sec A – cos A) = 1/(tan A + cot A)

10. If a sin θ + b cos θ = c, prove that a cosθ – b sinθ = √(a 2 + b 2 – c 2 ).

a 2 sin 2 θ + b 2 cos 2 θ + 2ab sin θ cos θ = c 2

a 2 (1 – cos 2 θ) + b 2 (1 – sin 2 θ) + 2ab sin θ cos θ = c 2

a 2 – a 2 cos 2 θ + b 2 – b 2 sin 2 θ + 2ab sin θ cos θ = c 2

a 2 + b 2 – c 2 = a 2 cos 2 θ + b 2 sin 2 θ – 2ab sin θ cos θ

a 2 + b 2 – c 2 = (a cos θ – b sin θ ) 2

⇒ a cos θ – b sin θ = √(a 2 + b 2 – c 2 )

## Video Lesson on Trigonometry

## Practice Questions on Trigonometry

Solve the following trigonometry problems.

- Prove that (sin α + cos α) (tan α + cot α) = sec α + cosec α.
- If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B.
- If sin θ + cos θ = √3, prove that tan θ + cot θ = 1.
- Evaluate: 2 tan 2 45° + cos 2 30° – sin 2 60°
- Express cot 85° + cos 75° in terms of trigonometric ratios of angles between 0° and 45°.

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## 250+ Trigonometry Questions with Solution Free PDF For SSC, RRB, FCI Exams – Download Now

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quadrants. Since cosine is negative in the II and III quadrants, the solutions for this equation occur in those quadrants. Find the reference angle T' for the solutions T: 2 3 s T 2 3 s T' 2 6 3 ' s 1 S T The solutions in the II quadrant: The one solution in the II quadrant, that is between 0 and 2S, is 6 5 6 S S T S . Now, all the other ...

(This is explained in more detail in the handout on inverse trigonometric functions.) Use the INV ndkey (or 2 function key) and the SIN key with 2 1 to get an answer of 30q. Example 3: Solve for x : 3 sin x 2sin x cos x 0, 0d x 2S. Solution : Factor the expression on the left and set each factor to zero. sin x 3 2sin x cos x 0 sin x

Angles in all four quadrants A LEVEL LINKS Scheme of work: 4a. Trigonometric ratios and graphs Key points • The sine, cosine and tangent of some angles may be written exactly. 0 30° 45° 60° 90° sin 10 1 cos 1 3 0 tan 30 1 • You can use these rules to find sin, cos and tan of any positive or negative angle using the

Identify the quadrants for the solutions on the interval [0, 2π) Cosine is negative in quadrants II and III . Solve for the angle 4x . Cosine is equal to . 1 2. at 3 π so the angles in quadrants II and III are π - 3. π = 2 3 π (quadrant II) and π + 3 π = 4 3 π (quadrant III) 4x = 2 3. π and 4x = 4 3 π Add 2nπ to the angle and solve ...

TRIGONOMETRY PRACTICE TEST This test consists of 20 questions. While you may take as much as you wish, it is expected that you are able to complete it in about 45 minutes. For proper course placement, please: • Take the test seriously and honestly • Do your own work without any assistance. Do not use any reference materials,

Trig Functions and the Four Quadrants Quadrant II 90 < < 180 Sine values for angles whose terminal side fall in this quadrant are positive, because the y - values in this quadrant are positive Cosine and Tangent values for angles whose terminal side fall in this quadrant are negative because the x-values in this quadrant are negative

Trig Section 5.1: Graphing the Trigonometric Functions / Unit Circle MULTIPLE CHOICE. Solve the problem. 1) What is the domain of the cosine function? 1) A) all real numbers, except integral multiples of (180 °) B) all real numbers C) all real numbers, except odd multiples of 2 (90 °) D) all real numbers from - 1 to 1, inclusive

Unit Circle Trigonometry Coordinates of Quadrantal Angles and First Quadrant Special Angles x y 1 -1 1 -1 0o 90o 180o 270o 360o 30o 120o 60o 150o 210o 240o 300o 330o 135o 45o 225o 315o Putting it all together, we obtain the following unit circle with all special angles labeled:

7. Application of Trigonometry on the Cartesian Plane In this video we apply what we know about trigonometric ratios on the Cartesian Plane. We determine lengths of sides by sketching a right angle triangle in the correct quadrants

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Trignometry Study Materials PDF With Practice Questions Worksheet is available here to download in English and Hindi language. Trigonometry is the branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of any angles.

knowledge and skills in working with basic concepts in trigonometry and the graphs of trigonometric functions. While studying these slides you should attempt the 'Your Turn' questions in the slides. After studying the slides, you should attempt the ... 5.1.6 Apply the correct signs for the ratios in each of the four quadrants

Explore the surplus collection of trigonometry worksheets that cover key skills in quadrants and angles, measuring angles in degrees and radians, conversion between degrees, minutes and radians, understanding the six trigonometric ratios, unit circles, frequently used trigonometric identities, evaluating, proving and verifying trigonometric …

0/1900 Mastery points Unit circle introduction Radians The Pythagorean identity Special trigonometric values in the first quadrant Trigonometric values on the unit circle Graphs of sin (x), cos (x), and tan (x) Amplitude, midline, and period Transforming sinusoidal graphs Graphing sinusoidal functions Sinusoidal models Long live Tau

The Pythagorean identity. Trigonometric values of special angles. Quiz 1: 5 questions Practice what you've learned, and level up on the above skills. Graphs of sin (x), cos (x), and tan (x) Amplitude, midline and period. Transforming sinusoidal graphs. Quiz 2: 6 questions Practice what you've learned, and level up on the above skills.

How To Download the Trigonometry PDF Free? Follow below steps :- Step 1: Click on the download now button. You will be taken to ExamsCart download page. Step 2: On that topic page click on save button. Step 3: After that click on that link than automatically the PDF will be downloaded.

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In quadrant III, the reference angle is θ ′ ≈ π − 1.8235 ≈ 1.3181. The other solution in quadrant III is θ ′ ≈ π + 1.3181 ≈ 4.4597. The solutions are θ ≈ 1.8235 ± 2πk and θ ≈ 4.4597 ± 2πk. Exercise 3.3.3 Solve cosθ = − 0.2. Answer Solving Trigonometric Equations in Quadratic Form

Trigonometry Question with Solution Free PDF As questions are based on previous year papers, there are chances that candidates will find many questions from the Trigonometry Questions PDF in all competitive Exams.

Practice Questions. 1. If sides a and b of a right triangle are 8 and 6, respectively, find cosine of α. 2. Find tangent of a right triangle, if a is 3 and c is 5. 3. If α=300, find sin300 + cos600. 4. Calculate (sin2300 - sin00)/ (cos900 - cos600).

Trigonometry Questions and Answers 1. From the given figure, find tan P - cot R. Solution: From the given, PQ = 12 cm PR = 13 cm In the right triangle PQR, Q is right angle. By Pythagoras theorem, PR 2 = PQ 2 + QR 2 QR 2 = (13) 2 - (12) 2 = 169 - 144 = 25 QR = 5 cm tan P = QR/PQ = 5/12 cot R = QR/PQ = 5/12 So, tan P - cot R = (5/12) - (5/12) = 0 2.

Multiple Choice Trigonometry and Trigonometry Ratio Sample Paper: Ques. If cos x + cos 2 x = 1, then the value of sin 2 x + sin 4 x is. Ques. If tan A + cot A = 4, then tan 4 A + cot 4 A is equal to. Ques. A circular wire of radius 7 cm is cut and bend again into an arc of a circle of radius 12 cm. The angle subtended by the arc at the centre is.

250+ Trigonometry Questions with Solution Free PDF For SSC, RRB, FCI ...