Are these practice questions for Trigonometric Functions based on the CBSE pattern?

Yes. Every practice question is modeled on the CBSE Class 11 - Science Mathematics exam pattern — including MCQs, assertion-reason questions, and short-answer formats that frequently appear in CBSE papers.

Are the practice questions for Trigonometric Functions free?

Yes. Every chapter includes free practice questions for Class 11 - Science students to get you started.

What types of questions are included?

The practice set for Trigonometric Functions 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 Trigonometric Functions for full coverage.

How many practice questions are there for Trigonometric Functions?

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

Trigonometric Functions Class 11 Mathematics Practice Questions with Answers

easy

Convert the angle

\frac{11\pi}{12}

radians into degree measure.

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easy

Calculate the value of

\cos(-750^\circ)

.

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easy

Define the term radian measure as it relates to an angle in a circle.

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easy

State the value of sin(π) and cos(π/2).

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easy

Calculate the degree measure of an angle that is 5π/12 radians.

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easy

Recall the formula for tan(x - y).

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easy

State the formula that expresses the relationship between degree measure and radian measure.

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easy

Calculate the value of

\sin 75^\circ + \sin 15^\circ

.

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easy

A pendulum of length 50 cm swings through an angle. If its tip describes an arc of length 10 cm, calculate the angle of the swing in radians.

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easy

Examine the following statement and state if it is true or false: The equation sin(x) = 2 has a real solution for x.

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easy

Name the six trigonometric functions and list their reciprocal pairs.

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medium

Recall the formula for sin(2x) in terms of both sine/cosine and in terms of tangent.

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medium

List the signs of all six trigonometric functions when an angle's terminal side lies in the third quadrant.

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medium

If

\tan x = -\frac{4}{3}

and

x

lies in the second quadrant, analyze the signs to find the value of

\sin x

.

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medium

Calculate the value of cosec(-1110°).

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medium

Two wheels are rotated. The first turns through 6 radians in a second, while the second turns through 450 revolutions per minute. Compare their angular speeds and determine which wheel is rotating faster.

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medium

Calculate the length of an arc of a circle with a radius of 14 cm that subtends an angle of

45^\circ

at the center. (Use

\pi = \frac{22}{7}

)

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medium

If

\sec x = -\frac{13}{12}

and

\frac{\pi}{2} < x < \pi

, calculate the value of the expression

2 \sin x + 3 \cos x

.

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medium

Analyze the expression tan(x) + cot(x) and demonstrate that it can be simplified to 2cosec(2x).

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medium

Describe the domain and range of the standard tangent function, y = tan x.

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medium

If

\sin A = \frac{4}{5}

and

A

is in the second quadrant, calculate the value of

\sin 2A

.

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medium

If

\cos x = -\frac{3}{5}

and

x

lies in the third quadrant (

\pi < x < \frac{3\pi}{2}

), analyze the quadrant of

\frac{x}{2}

and calculate the values of

\sin(\frac{x}{2})

,

\cos(\frac{x}{2})

, and

\tan(\frac{x}{2})

.

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medium

The hour hand of a clock is 6 cm long. Calculate the distance its tip moves in 20 minutes. (Use

\pi = 3.14

)

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medium

If sin(x) = -4/5 and x lies in the third quadrant, solve for the values of tan(x) and sec(x).

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medium

Demonstrate that

(\cos x + \cos y)^2 + (\sin x + \sin y)^2 = 4 \cos^2\left(\frac{x-y}{2}\right)

.

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medium

Explain the convention used to determine if an angle is positive or negative.

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medium

Given tan(θ) = 3/4 and θ lies in the third quadrant, calculate the value of cos(2θ).

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medium

Arcs of the same length in two circles subtend angles of

120^\circ

and

75^\circ

at their centers. Analyze the relationship to find the ratio of their radii.

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medium

Identify the intervals between 0 and 2π where the cosine function is positive and where it is negative.

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medium

Demonstrate the calculation of the exact value of tan(105°) by applying the sum identity for tangent.

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medium

Recall the sum-to-product formula for cos x + cos y.

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medium

Explain the concept of quadrantal angles and provide two examples in degrees.

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medium

Apply a suitable identity to demonstrate that the expression sin(75°) - sin(15°) is equal to cos(45°).

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medium

Convert

-22^\circ 30'

into radian measure.

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medium

Calculate the radius of a circle where a central angle of 60° intercepts an arc of length 44 cm. Use π = 22/7.

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medium

Summarize the relationship between the length of a circular arc, the radius of the circle, and the central angle subtended by the arc.

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hard

Demonstrate the proof of the trigonometric identity: (cos(4x) + cos(3x) + cos(2x)) / (sin(4x) + sin(3x) + sin(2x)) = cot(3x).

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hard

Solve the equation 2cos^2(x) + 3sin(x) - 3 = 0 for principal values of x.

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hard

Calculate the value of

\tan 105^\circ

by expressing it as a sum of two standard angles.

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hard

If tan(x) = -4/3 and x lies in the second quadrant, solve for the values of sin(x/2) and cos(x/2).

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hard

Calculate the value of the expression

\cos 20^\circ \cos 40^\circ \cos 80^\circ

.

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hard

If sin(A) = 5/13 and cos(B) = 4/5, where A is in the second quadrant and B is in the fourth quadrant, calculate the value of sin(A - B).

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hard

State the fundamental Pythagorean identity for trigonometry and explain how the other two Pythagorean identities are derived from it.

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hard

Calculate the value of the product

\sin 10^\circ \sin 30^\circ \sin 50^\circ \sin 70^\circ

.

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hard

List the four different formulas for cos(2x) given in the chapter.

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Trigonometric FunctionsClass 11 Mathematics Practice Questions