Find sin(2x), cos(2x), and tan(2x) from the given information. tan(x) = - 15/8 , x in quadrant II

Solution:

Consider tan x = t

Use the trigonometric identity

cos 2x = (1 - t²)/(1 + t²)

Substituting the values

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

cos 2x = -161/289

sin 2x = 2t/(1 + t²)

sin 2x = 2 (-15/8)/(289/64)

sin 2x = -30 8/289

sin 2x = -240/289

We know that

tan 2x = sin2x/cos2x

Substituting the values

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

tan 2x = 240/161

Therefore, sin(2x), cos(2x), and tan(2x) is -240/289, -161/289 and 240/161.

Find sin(2x), cos(2x), and tan(2x) from the given information. tan(x) = - 15/8 , x in quadrant II

Summary:

The value of sin(2x), cos(2x), and tan(2x) from the given information tan(x) = - 15/8 , x in quadrant II is -240/289, -161/289 and 240/161.