Suppose Start Fraction pi Over 2 End Fraction less-than theta less-than pi and sine ⁡ theta equals Start Fraction 2 Over 5 End Fraction period Evaluate cosine ⁡ theta.

Answer 1

I am going to guess that you meant:

sin Ø = 2/5, and π/2 < Ø ≤ π
or , even more simply stated ....

sin Ø = 2/5 and Ø is in the second quadrant

make a sketch of your right-angled triangle, with
y = 2, and r = 5
By Pythagoras: x^2 + y^2 = 5^2
x^2 + 4 = 25
x = -√21 in the 2nd quad

so cosØ = -√21/5