Are these practice questions for Introduction to Trigonometry based on the CBSE pattern?

Yes. Every practice question is modeled on the CBSE Class 10 Mathematics exam pattern — including MCQs, assertion-reason questions, and short-answer formats that frequently appear in CBSE papers.

Are the practice questions for Introduction to Trigonometry free?

Yes. Every chapter includes free practice questions for Class 10 students to get you started.

What types of questions are included?

The practice set for Introduction to Trigonometry mainly includes MCQs and CBSE-style short-answer questions, with instant feedback on each answer. For full-length textbook practice, use the NCERT Solutions page.

Are the practice questions suitable for board exam preparation?

Yes. The questions test the same concepts and depth that CBSE asks in board exams. After finishing, also solve the NCERT and NCERT Exemplar exercises for Introduction to Trigonometry for full coverage.

How many practice questions are there for Introduction to Trigonometry?

The number scales with chapter length and concept density. Each chapter typically has 15-50 practice questions across MCQ and short-answer formats.

Introduction to Trigonometry Class 10 Mathematics Practice Questions with Answers

easy

Name the Greek letter commonly used to denote an angle in trigonometry.

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easy

State the fundamental trigonometric identity involving

\sin^2 A

and

\cos^2 A

.

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easy

Analyze and compare the values of

\sin \theta

and

\cos \theta

as the angle

\theta

increases from

0^\circ

to

90^\circ

.

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easy

Recall the value of

\tan 45^{\circ}

.

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easy

Analyze the statement: "For some acute angle A,

\sec A = \frac{5}{12}

" and determine if it is possible. Justify your answer.

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easy

Propose a real-world scenario that can be modeled by a right-angled triangle where you need to find an unknown height. If the angle of elevation from a point 40 meters away from the base of the object is

60^{\circ}

, formulate the trigonometric equation needed to solve for the height and find its value.

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easy

Create an expression using trigonometric ratios of

30^{\circ}

and

60^{\circ}

that simplifies to exactly 1.

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easy

Justify why

\tan A

is not defined for

A = 90^{\circ}

by using the relationship

\tan A = \frac{\sin A}{\cos A}

.

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easy

List the six trigonometric ratios for an acute angle A.

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easy

In a right-angled triangle ABC, with the right angle at B, if the side

AB = 7

cm and

\angle ACB = 30^\circ

, apply trigonometric ratios to calculate the lengths of the sides BC and AC.

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easy

Define the trigonometric ratio sine for an acute angle

\theta

in a right-angled triangle.

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medium

Given a right-angled triangle with a hypotenuse of length

10

cm and one acute angle of

30^{\circ}

, recall the formula for sine and calculate the length of the side opposite to the

30^{\circ}

angle.

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medium

Two students, Rohan and Priya, are asked to evaluate

\frac{5\cos^2 60^{\circ} + 4\sec^2 30^{\circ} - \tan^2 45^{\circ}}{\sin^2 30^{\circ} + \cos^2 30^{\circ}}

. Rohan simplifies the denominator to 1 using the identity

\sin^2\theta + \cos^2\theta = 1

and then calculates the numerator. Priya substitutes the values for all six trigonometric ratios and then calculates. Evaluate both methods. Which method is more efficient and why? Justify your choice and provide the complete calculation using the more efficient method.

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medium

In

\triangle ABC

, right-angled at B, if

AB = 5

cm and

BC = 12

cm, solve for the value of

\sin A \cos C + \cos A \sin C

.

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medium

Create a right-angled triangle problem where the hypotenuse is

15

cm and one of the acute angles is

\theta

such that

\cot \theta = \frac{4}{3}

. Formulate the steps to find the lengths of the other two sides.

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medium

A classmate states that if

\cos A = \cos B

, then it always implies

A = B

. Justify the conditions under which this statement is true for acute angles A and B, referencing the properties of trigonometric ratios.

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medium

Recall the values of

\sin 60^{\circ}

,

\cos 30^{\circ}

, and

\tan 30^{\circ}

.

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medium

In a right-angled triangle ABC, with the right angle at B, apply the Pythagoras theorem to demonstrate the derivation of the identity

1 + \cot^2 A = \text{cosec}^2 A

.

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medium

In a right-angled triangle PQR, right-angled at Q, identify the side opposite to angle P, the side adjacent to angle P, and the hypotenuse.

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medium

Evaluate the statement: 'The identity

\sec^2 A - \tan^2 A = 1

is derived from the Pythagorean theorem and holds true for all angles A.' Critique this statement by identifying any limitations on the angle A, and provide a complete proof of the identity with these limitations.

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medium

Formulate a problem involving a right-angled triangle where the value of

\tan A = \frac{5}{12}

is given, and the task is to find the value of the expression

\frac{\sin A + \cos A}{\sec A - \cot A}

. Solve the problem you created.

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medium

Analyze the expression

\frac{\sin \theta - 2 \sin^3 \theta}{2 \cos^3 \theta - \cos \theta}

and demonstrate that it simplifies to

\tan \theta

.

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medium

Explain the relationship between cosecant, secant, and cotangent with sine, cosine, and tangent respectively.

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medium

Justify why the value of

\sin \theta

increases as

\theta

increases from

0^{\circ}

to

90^{\circ}

by considering a right-angled triangle with a fixed hypotenuse.

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medium

Describe the process to find all other trigonometric ratios for an angle A if you are given that

\tan A = \frac{3}{4}

.

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medium

Given that

5 \cot \theta = 3

, apply this to calculate the value of

\frac{6 \sin \theta - 3 \cos \theta}{7 \sin \theta + 3 \cos \theta}

.

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medium

Explain how the values of

\sin \theta

and

\cos \theta

change as the angle

\theta

increases from

0^{\circ}

to

90^{\circ}

. Summarize the values at

0^{\circ}

,

30^{\circ}

,

45^{\circ}

,

60^{\circ}

, and

90^{\circ}

for both ratios.

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medium

Solve for the acute angles A and B if it is given that

\tan(A - B) = \frac{1}{\sqrt{3}}

and

\sin(A + B) = \frac{\sqrt{3}}{2}

, where

A > B

.

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medium

Examine whether the equation

\frac{1 - \tan^2 A}{1 + \tan^2 A} = \cos^2 A - \sin^2 A

is a trigonometric identity for all acute angles A.

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medium

Propose a method to determine the values of A and B if you are given the equations

\sin(A+B) = 1

and

\cos(A-B) = \frac{\sqrt{3}}{2}

, with the constraints that

0^{\circ} < A+B \le 90^{\circ}

and

A>B

. Justify each step of your proposed method and find the values.

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medium

If

\sec \theta = \frac{13}{5}

, apply this information to calculate the value of the expression

\frac{2 \sin \theta - 3 \cos \theta}{4 \sin \theta - 9 \cos \theta}

.

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medium

Calculate the exact numerical value of the expression

5 \sin^2 30^\circ + \cos^2 45^\circ - 4 \tan^2 30^\circ

.

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hard

List the three fundamental trigonometric identities and for each identity, specify the range of angle values for which it is true.

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hard

Analyze and prove the following trigonometric identity:

\frac{\cos A}{1 - \tan A} + \frac{\sin A}{1 - \cot A} = \sin A + \cos A

.

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hard

Evaluate the following proof that claims

1 = -1

: Step 1:

\cos^2 x = 1 - \sin^2 x

Step 2:

\sqrt{\cos^2 x} = \sqrt{1 - \sin^2 x}

Step 3:

\cos x = (1 - \sin^2 x)^{1/2}

Let

x = 180^{\circ}

. Step 4:

\cos 180^{\circ} = (1 - \sin^2 180^{\circ})^{1/2}

Step 5:

-1 = (1 - 0)^{1/2} = \sqrt{1} = 1

Identify the flaw in the reasoning, specifically concerning the properties of square roots.

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hard

In

\triangle PQR

, right-angled at Q, it is given that

PR + QR = 25

cm and

PQ = 5

cm. Solve for the values of

\sin P

,

\cos P

, and

\tan P

.

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hard

Explain why the value of

\tan 90^{\circ}

is not defined.

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hard

If

\sin A = \frac{5}{13}

, recall the formula for

\cos A

using a trigonometric identity and find its value.

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hard

Formulate a proof for the identity

\frac{\cos A}{1 - \tan A} + \frac{\sin A}{1 - \cot A} = \sin A + \cos A

. Your proof should clearly state each algebraic and trigonometric step.

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hard

Demonstrate that

(\text{cosec } A - \sin A)(\sec A - \cos A) = \frac{1}{\tan A + \cot A}

.

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hard

Is the statement '

\sin A

is the product of 'sin' and A' true? Explain your answer.

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hard

For an acute angle

\theta

, solve the equation

2 \cos^2 \theta + 3 \sin \theta = 3

.

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hard

A student attempted to solve the equation

\sin(2\theta) = \frac{\sqrt{3}}{2}

for an acute angle

\theta

. Their steps were: Step 1:

2\sin(\theta) = \frac{\sqrt{3}}{2}

Step 2:

\sin(\theta) = \frac{\sqrt{3}}{4}

Step 3:

\theta = \arcsin(\frac{\sqrt{3}}{4})

Critique the student's method, identify the fundamental error in their reasoning, and provide the correct step-by-step solution.

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hard

Evaluate whether it is possible to construct a right-angled triangle where

\sec \theta = \frac{x^2+y^2}{2xy}

for distinct positive real numbers

x

and

y

. Justify your answer.

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hard

A student claims that for any acute angle

\theta

, the value of

\sin \theta + \cos \theta

is always greater than 1. Justify whether this claim is true or false by evaluating the expression for

\theta = 30^{\circ}

,

\theta = 45^{\circ}

, and considering the general case by squaring the expression.

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Introduction to TrigonometryClass 10 Mathematics Practice Questions