basic identities

Question

what is sinΘ when secΘ= √5

Answer 1

Use A to mean θ.

If sec(A) = sqrt(5), then cos(A) = 1/sqrt(5).

Since sin²(A) + cos²(A) = 1, then

sin²(A) = 1 - cos²(A)

= 1 - ( 1 / sqrt(5) )²

= 1 - 1/5

= 4/5

Therefore,

sin(A) = ± 2 / sqrt(5) = ± (2/5) * sqrt(5), ans.