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CBSE - Class 11 Mathematics Trigonometric Functions Worksheet

Find the value of: (i) $\sin 75^{\circ}$

Find the values of the trigonometric functions: $\sin (-\frac{11\pi}{3})$

A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?

Prove the following: $\frac{\sin x + \sin 3x}{\cos x + \cos 3x} = \tan 2x$

Find the values of the trigonometric functions: $\cot (-\frac{15\pi}{4})$

Prove that: $2\sin^2 \frac{3\pi}{4} + 2\cos^2 \frac{\pi}{4} + 2\sec^2 \frac{\pi}{3} = 10$

Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm (Use $\pi = \frac{22}{7}$).

Prove that: $\sin x + \sin 3x + \sin 5x + \sin 7x = 4 \cos x \cos 2x \sin 4x$

Find the values of other five trigonometric functions if $\sec x = \frac{13}{5}$, $x$ lies in fourth quadrant.

10.

Prove the following: $\frac{\tan(\frac{\pi}{4} + x)}{\tan(\frac{\pi}{4} - x)} = (\frac{1+\tan x}{1-\tan x})^2$

11.

If in two circles, arcs of the same length subtend angles $60^{\circ}$ and $75^{\circ}$ at the centre, find the ratio of their radii.

12.

Prove the following: $\cos (\frac{\pi}{4} - x) \cos (\frac{\pi}{4} - y) - \sin (\frac{\pi}{4} - x) \sin (\frac{\pi}{4} - y) = \sin (x+y)$

13.

Prove that: $\frac{(\sin 7x + \sin 5x) + (\sin 9x + \sin 3x)}{(\cos 7x + \cos 5x) + (\cos 9x + \cos 3x)} = \tan 6x$

14.

Find $\sin \frac{x}{2}$, $\cos \frac{x}{2}$ and $\tan \frac{x}{2}$ in each of the following : $\sin x = \frac{1}{4}$, $x$ in quadrant II

15.

Prove the following: $\cos^2 2x - \cos^2 6x = \sin 4x \sin 8x$

16.

In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of the chord.

17.

Find $\sin \frac{x}{2}$, $\cos \frac{x}{2}$ and $\tan \frac{x}{2}$ in each of the following : $\cos x = -\frac{1}{3}$, $x$ in quadrant III

18.

Find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes an arc of length (i) 10 cm

19.

Prove the following: $\frac{\cos 4x + \cos 3x + \cos 2x}{\sin 4x + \sin 3x + \sin 2x} = \cot 3x$

20.

Prove the following: $\cos(\frac{3\pi}{4} + x) - \cos(\frac{3\pi}{4} - x) = -\sqrt{2} \sin x$

CBSE - Class 11 Mathematics Trigonometric Functions Worksheet

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