College Pre-Calculus

Question

Suppose theta and phi are in the first quadrant and that cos(theta)=5/13 and csc(phi)=15/4. Then, determine the following: sec(pi/2 - phi) = ? And sin(90 - theta) = ?

Answer 1

you can determine (by Pythag. identity) that θ  = 12/13 and sin φ = 4/15 and cos φ = √209/15.

Now use the formulas for sin (a-b) and cos (a-b). The reciprocal of cos(a-b) is, of course, sec(a-b).

Answer 2

sin (90 - θ) = cos θ, look at problem

sec (π/2 - φ) = 1 / (sin (π/2 - φ)

                    = 1 / cos φ, look at problem