Question

How do you find the product of all six trigonometric functions of an angle theta in standard position whose terminal side passes through `(- sqrt 3, 1)`?

Answer 1

Find values of trig functions

Explanation:

Consider the right triangle OMm with
`Om = -sqrt3`; and Mn = 1.
The hypotenuse OM equals to: `OM = sqrt(1 + 3) = 2`
Call t the angle < Mom.
`sin t = 1/2`
`cos t = sqrt3/2`
`tan t = sin t/(cos t) = 1/sqrt3 = sqrt3/3`
`cot t = sqrt3`
`sec t = 2/sqrt3 = 2sqrt3/3`
`csc t = 2`