Question

Which expressions are equivalent?

I. cos  θ

II. cos (-θ )

III. sin (-θ)/tan(-θ)

Answers:

A. I and II

B. II and III

C. I and III

D. I, II, and III

Answer 1

(I) cosθ

(II) cosθ=cos(-θ); so I and II are the same.

(III) tan(-θ)=sin(-θ)/cos(-θ)=-tanθ, because sin(-θ)=-sinθ and cos(-θ)=cosθ;

so sin(-θ)/tan(-θ)=-sinθ/-tanθ=sinθ/tanθ=sinθcosθ/sinθ=cosθ, same as (I) and (II).

All three are the same: answer D.

Answer 2

C. That was based on even-odd identities