basic identities

Question

what is tanΘ when secΘ=5

Answer 1

sec(θ) = hyp/adj so the triangle would look like either of these:

Using the Pythagorean Theorem, we can solve for the "opposite" side:

opp = √(5² - 1²) = √24 = 2√6 but, as you can see, it can either be +2√6 or -2√6 because it can either go up or it can go down.

So tan(θ) = opp/adj = either 2√6/1 = 2√6 or -2√6/1 = -2√6

Answer 2

Use the relationships between the sides of a right triangle to solve these (draw and label a diagram!).

sec θ = 5

cos θ = 1/5

sin θ = √24 / 5

tan θ = √24