Question

Find the Value of cosx if :
sinx/2=4/5

x/2 is in the second quadrant .

Answer is :
1) -3/25
2) -7/25
3) -9/25
4) -8/25

Answer 1

Answer

cos x/2 will be negative since the angle x/2 lies in the second quadrant .

Given , sin x/2 = 4/5

We know that :

sin x/2 = ± √( 1 - cos x ) / √2

⇒ 4/5 = - √( 1 - cos x )/√2

Upon squaring both sides we get :

⇒ 16/25 = ( 1 - cos x ) / 2

⇒ 32/25 = 1 - cos x

Transpose cos x :

⇒ cos x = 1 - 32/25

⇒ cos x = ( 25 - 32 ) / 25

⇒ cos x = - 7/25

Option 2 is correct .

Explanation

There are 4 quadrants in the coordinate system .

The first quadrant starts from 0° - 90° .

The second quadrant starts from 90° - 180° .

The third quadrant starts from 180° - 270° .

The fourth quadrant starts from 270°- 360° .

ALL-SIN-TAN-COS Rule

All ratios are positive in the first quadrant .

The ratio of sine is positive in the second quadrant .

The ratio of tan is positive in the third quadrant .

The ratio of cos is positive in the fourth quadrant

Answer 2

ANSWER:--------

In the attachment

hope it helps:-

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