Question

How do you find the exact values of the six trigonometric function of `theta` if the terminal side of `theta` in the standard position contains the point `(sqrt2,-sqrt2)`?

Answer 1

Find values of trig functions

Explanation:

The point M `(sqrt2, -sqrt2)` is located at extremity of arc `(-pi)/4` Quadrant IV, on the trig circle with diameter R = 2.
(Right triangle formula: `R^2 = (sqrt2)^2 + (sqrt2)^2 = 4` --> R = 2)
`sin t = -sqrt2/R = - sqrt2/2`
`cos t = sqrt2/2`
`tan t = sin/(cos) = - 1`
`cot t = 1/(tan) = - 1`
`sec t = 1/(cos) = 2/sqrt2 = sqrt2`
`csc t = 1/(sin) = - sqrt2`