Question

Use the Pythagorean identities rather than reference triangles . Find tanθ and cotθ if secθ = 5/2 and sinθ <0.

Please help ! Much appreciated !!

Answer 1

Given any one trigonometric relation, you can obtain the other five using simple identities.

If secθ = 5/2,

(secθ)^2 = (tanθ)^2 + 1 (Trigonometric Identity)
=> (5/2)^2 = (tanθ)^2 + 1
=> 25/4 - 1 = (tanθ)^2
=> 21/4 = (tanθ)^2

If sinθ is negative, and cosθ is positive,

=> tanθ = -(root(21/4))

Now, cotθ = (1/tanθ)
= (1/(21/4))
= -(root(4/21))