If cos (2x) = 45 and x terminates in quadrant 1, then find the sin (x).

Answer 1

I assume you meant cos(2x) = 4/5

cos(2x)= cos²(x)-sin²(x) by cosine double angle formula

= 1-sin²(x)-sin²(x)

1-2sin²(x) =4/5

2sin²(x)=1/5

sin²(x)=1/10

sin(x)=√10/10 which is in Q1