Find sin 2x, cos 2x, and tan 2x from the given information.

Question

tan x = −12/5, x in Quadrant II?

Answer 1

tanx = -12/5

From the basic trigonometric ratios, tan(θ) = (opposite side/adjacent side)

From Pythagorean theorem,

Hypotenuse = √[(opposite side)² + (adjacent side)²]

= √(12² + 5²) = √169

= 13

x in second quadrant.

sinx = opposite side/hypotenuse 

sinx = 12/13

cosx = -5/13

Sin(2x) = 2 sinx cosx

= 2 (12/13)(-5/13)

sin(2x) = - 120/169

 

cos(2x) = cos²x - sin²x

= (-5/13)² - (12/13)²

= (25/169) - (144/169)

cos(2x) = - 119/169

 

tan(2x) = sin(2x)/cos(2x)

= (-120/169)/(-119/169)

tan(2x) = 120/119.