Find sin(2x), cos(2x), and tan(2x) from the given information. sin(x) = 8 / 17 , x in quadrant I

Solution:

Given, sin(x) = 8/17

We have to find the value of sin(2x), cos(2x), and tan(2x) in the first quadrant.

We know, sin²x + cos²x = 1

(8/17)² + cos²x = 1

cos²x = 1 - (64/289)

cos²x = 225/289

Taking square root,

cos x = ±15/17

In the first quadrant cos x has to be positive.

Thus, cos x = +15/17

Now, sin 2x = 2 sinx cosx

sin 2x = 2(8/17)(15/17)

sin 2x = 240 / 289

We know, cos 2x = cos²x - sin²x 

cos 2x = (15/17)² - (8/17)²

cos 2x = (225 / 289) - (64 / 289)

cos 2x = (225 - 64) / 289

cos 2x = 161 / 289

We know, tan 2x = sin 2x / cos 2x

tan 2x = (240 / 289)/(161 / 289)

tan 2x = 240 / 161

Therefore, the values of sin 2x, cos 2x and tan 2x are 240 / 289, 161 / 289 and 240 / 161.

Find sin(2x), cos(2x), and tan(2x) from the given information. sin(x) = 8 / 17 , x in quadrant I

Summary:

The values of sin 2x, cos 2x and tan 2x from the given information sin(x) = 8/17 , x in quadrant I are 240 / 289, 161 / 289 and 240 / 161 in the first quadrant.