sin(θ)=1/8, Find exact values (as fractions, not decimal approximations) for the following. (a) cos(π2−θ) = help (fractions) (b) sec(π2−θ) =

Question

Suppose sin(θ)=1/8, where θ is in radians. Find exact values (as fractions, not decimal approximations) for the following.

(a) cos(π2−θ) =

(b) sec(π2−θ) =

Answer 1

Using the Pythagorean identity (sum of squares of sine & cosine = 1) and assuming θ to be in the first quadrant, then cos θ = √63 / 8.

 

Therefore (a) cos(π2−θ) = - √63 / 8.

 

b) secant will be reciprocal of the above cosine value.