Ways functions can be expressed

Question

What are some of the ways  can be expressed? 

Answer 1

Right triangles.

tanα=sinα/cosα=(a/c)/(b/c)=a/b

tanβ=sinβ/cosβ=(b/c)/(a/c)=b/a

Answer 2

I believe the question is simply asking you to re-arrange that equation to get 2 different ones.

Basically solve for sin(θ) and cos(θ).

What is sin(θ) equal to in terms of cos(θ) & tan(θ)?

What is cos(θ) equal to in terms of sin(θ) & tan(θ)?

Hint: One of those two is a fraction, while the other is a product.