Question

Suppose that tand cos t =q. Express the values ofthe five trigonometric

functions at t in terms of q.

Answer 1

Five trigonometric functions.

Explanation:

We are given the following information in the question:

`\cos t = q`

We have to find the values of the five trigonometric functions at t in terms of q.

`\sin^2 t + \cos^2 t = 1\\\sin^2 t + q^2 = 1\\\sin^2 t = 1-q^2\\\sin t = √(1-q^2)`

`\csc t = \displaystyle(1)/(\sin t) = (1)/(√(1-q^2))\\\\\sec t = (1)/(\cos t) = (1)/(q)\\\\\tan t = (\sin t)/(\cos t) = (√(1-q^2))/(q)\\\\\cot t = (1)/(\tan t) = (q)/(√(1-q^2))`