Q1 Find the radian measures corresponding to the following degree measures:

(i) 25 \degree
(ii)-47 \degree30'
(iii) 240\degree
(iv)520\degree

Q(2) Find the degree measures corresponding to the following radian measures.  (Use \small \pi =\frac{22}{7})

 \small (i) \frac{11}{16}
\small (ii) -4
\small (iii) \frac{5\pi }{3}
\small (iv) \frac{7\pi }{6}

Q 3)  A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?

Q (4)  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 \small \pi =\frac{22}{7} ) 

Q (5) In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of the chord.

Q (6) If in two circles, arcs of the same length subtend angles 60° and 75° at the centre, find the ratio of their radii.

Q (7) 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
(ii) 15 cm
(iii) 21 cm

Q (1) Find the values of other five trigonometric functions

\small \cos x = -\frac{1}{2}  , x lies in third quadrant.

Q (2) Find the values of other five trigonometric functions

\small \sin x = \frac{3}{5}  x lies in second quadrant.

Q (3) Find the values of other five trigonometric functions

\small \cot x = \frac{3}{4}  , x lies in third quadrant.

Q (4) Find the values of other five trigonometric functions

\small \sec x = \frac{13}{5}  , x lies in fourth quadrant.

Q (5) Find the values of the other five trigonometric functions

\small \tan x = -\frac{5}{12}  , x lies in second quadrant.

Q (6) Find the values of the trigonometric functions

\small \sin 765\degree

Q (7) Find the values of the trigonometric functions

\small cosec \ (-1410\degree)

Q (8) Find the values of the trigonometric functions

\small \tan \frac{19\pi }{3}

Q (9) Find the values of the trigonometric functions

\sin\left ( -\frac{11\pi}{3} \right )

Q (10)  Find the values of the trigonometric functions

\small \cot \left ( -\frac{15\pi }{4} \right )

Prove that 

Q(1) \small \sin ^{2} \left ( \frac{\pi }{6} \right ) + \cos ^{2}\left ( \frac{\pi }{3} \right ) - \tan ^{2}\left ( \frac{\pi }{4} \right ) = -\frac{1}{2}

Prove that 

Q(2). \small 2\sin ^{2}\left ( \frac{\pi }{6} \right ) + cosec ^{2}\left ( \frac{7\pi }{6} \right )\cos ^{2}\frac{\pi }{3} = \frac{3}{2}

Prove that 

Q(3) \small \cot ^{2}\left ( \frac{\pi }{6} \right ) + \csc \left ( \frac{5\pi }{6} \right ) + 3\tan ^{2}\left ( \frac{\pi }{6} \right ) = 6

Prove that 

Q(4) \small 2\sin ^{2}\left ( \frac{3\pi }{4} \right ) + 2\cos ^{2}\left ( \frac{\pi }{4} \right ) + 2\sec ^{2}\left ( \frac{\pi }{3} \right ) = 10

Q (5) Find the value of 

\small (i) \sin 75\degree

Q (5) Find the value of 

\small (ii) \tan 15\degree

Prove the following:

Q(6) \small \cos \left ( \frac{\pi }{4}-x \right )\cos \left ( \frac{\pi }{4}-y \right ) - \sin \left ( \frac{\pi }{4} -x\right )\sin \left ( \frac{\pi }{4}-y \right ) =\sin (x+y)
 

Q (7)  Prove the following

\small \frac{\tan \left ( \frac{\pi }{4}+x \right )}{\tan \left ( \frac{\pi }{4} -x\right )} = \left ( \frac{1+\tan x}{1-\tan x} \right )^{2}

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