Use the equivalent forms of the first Pythagorean identity I

Use the equivalent forms of the first Pythagorean identity. If cos theta = Squareroot/2 and theta terminates in QI, find sin theta. sin theta =

Solution

We have given cos(theta)=sqrt(3)/2

squaring both sides

cos²(theta)=3/4

We know the first pythagorean identity is sin²(theta)+cos²(theta)=1

sin²(theta) =1-cos²(theta) =1-(3/4) =1/4

sin(theta)=1/2