Question

θ is an angle in standard position that terminates in Quadrant II. If sinθ =2/3 , then cos2θ = _____.
1/9
4/9
8/9
4/3

Answer 1

we know that

sinθ =2/3
cos2θ=1-2 sin²θ---------> cos2θ=1-2*(2/3)²-----> 1-8/9------> 1/9

the answer is
cos2θ=1/9


let's check it by another method
sinθ =2/3----------> arcsin (2/3)--------> θ=41.81°
so
2θ=41.81*2--------> 2θ=83.62°
cos 2θ--------> cos 83.62°=0.1111--------> 1/9