if cos A = -4/5 for angle A in quadrant 2, find cos 2A?

Question

This problem is driving me insane. I have no idea where to start or how to do this.

Answer 1

CosA = -4/5

CosA = opposite side/hypotenuse

hypotenuse^2 = opposite side^2+ajacent side^2

25 =opposite side^2+16

opposite side^2 = 9

opposite side = 3

Sin A = 3/5

Cos2A = 1-2Sin^2A

= 1-2(9/25)

= 1-18/25

= - 7/25

 

Answer 2

cosA = -4/5

cosA = adjacent side / hypotenuse.

adjacent side = 4 and hypotenuse = 5

From pythagorean theorem hypotenuse²  = adjacent side² + opposite side²

25 = 16 + opposite side²

opposite side = √(25 - 16)

= 3

sinA = opposite side/hypotenuse

Since angle A in quadrant 2.

sinA = 3/5

cos 2A = 1 - 2sin² A = 1 - 2(3/5)²

= 1 - 2(9/25)

= 1 - 18/25

cos2A = 7/25