Suppose that sin Theta 1213 and that Theta is a Quadrant II

Suppose that sin Theta= 12/13 and that Theta is a Quadrant II angle. Find the exact value of cos Theta. Show work. Find the exact value of sin 2 Theta.. Show work. 24. Prove the identity (cos x + sin x)^2 - 1 = sin(2x)

Solution

23)sin=12/13

opposite side =12, hypotenuse =13

hypotenuse²=oppositeside²+Adjacent side²

13²=12²+Adjacent side²

169=144+Adjacent side²

Adjacent side²=169-144

Adjacent side²=25

Adjacent side=5

cos is negative in QII

=>cos=adjacentside/hypotenuse

=>cos=-5/13

b)sin2=2sincos

sin2=2(12/13)(-5/13)

sin2=-120/169