Question

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

Answer 1

Answer:

Five trigonometric functions.

Step-by-step 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.

$\sin^2 t + \cos^2 t = 1\\\sin^2 t + q^2 = 1\\\sin^2 t = 1-q^2\\\sin t = \sqrt{1-q^2}$

$\csc t = \displaystyle\frac{1}{\sin t} = \frac{1}{\sqrt{1-q^2}}\\\\\sec t = \frac{1}{\cos t} = \frac{1}{q}\\\\\tan t = \frac{\sin t}{\cos t} = \frac{\sqrt{1-q^2}}{q}\\\\\cot t = \frac{1}{\tan t} = \frac{q}{\sqrt{1-q^2}}$