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CBSE - Class 11 Mathematics Trigonometric Functions Worksheet

Find the radian measures corresponding to the following degree measures: (iv) $520^{\circ}$

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

Prove that: $2\sin^2 \frac{\pi}{6} + \text{cosec}^2 \frac{7\pi}{6} \cos^2 \frac{\pi}{3} = \frac{3}{2}$

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

Prove the following: $\cot x \cot 2x - \cot 2x \cot 3x - \cot 3x \cot x = 1$

Prove that: $\cot^2 \frac{\pi}{6} + \text{cosec} \frac{5\pi}{6} + 3\tan^2 \frac{\pi}{6} = 6$

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

Find the radian measures corresponding to the following degree measures: (iii) $240^{\circ}$

Prove the following: $\frac{\cos 9x - \cos 5x}{\sin 17x - \sin 3x} = -\frac{\sin 2x}{\cos 10x}$

10.

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.

11.

Find the radian measures corresponding to the following degree measures: (ii) $- 47^{\circ}30'$

12.

Prove that: $\sin 3x + \sin 2x - \sin x = 4\sin x \cos \frac{x}{2} \cos \frac{3x}{2}$

13.

Find the values of other five trigonometric functions if $\cot x = \frac{4}{3}$, $x$ lies in third quadrant.

14.

Find the values of the trigonometric functions: $\sin 765^{\circ}$

15.

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

16.

Prove the following: $\cot 4x (\sin 5x + \sin 3x) = \cot x (\sin 5x - \sin 3x)$

17.

Find the degree measures corresponding to the following radian measures (Use $\pi = \frac{22}{7}$). (i) $\frac{11}{16}$

18.

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

19.

Find the radian measures corresponding to the following degree measures: (i) $25^{\circ}$

20.

Find the values of other five trigonometric functions if $\sin x = \frac{3}{5}$, $x$ lies in second quadrant.

Worksheet Answers

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