If cos and theta 0.65 what is the value of sin and theta?

Remember use the Pythagorean Trig/ Identity.

Sin^(2)(Theta) + Cos^(2)(Theta) = 1

Algebraically rearrange

Sin^(2)(Theta) = 1 - Cos^(2)(Theta)

Substitute

Sin^(2)(Theta) = 1 - 0.65^(2)

Factor

Sin^(2)(Theta) = ( 1- 0.65 )( 1 + 0.65)

Sin^(2)(Theta) = (0.35)(1.65)

Sin^(2)(Theta) = 0.5775

Sin(Theta) = sqrt(0.5775)

Sin(Theta) = 0.759934207....

Theta = Sun^(-1)(0.759934207...)

Theta = 49.45839813 degrees.