Question

How do you use fundamental identities to find the values of the trigonometric values given angle in quadrant 4 such that csc (theta)= -5/2?

Answer 1

Find values of 6 trig functions

Explanation:

`csc t = - 5/2` --> `sin t = -2/5`.
Find `cos^2 t` by the identity: `cos^2 t = 1 - sin^2 t`
`cos ^2 t = 1 - 4/25 = 21/25` --> `cos t = +- sqrt21/5`
Since t in in Quadrant IV, then, cos t is positive -->
`cos t = sqrt21/5`
`tan t = sin/(cos) = (-2/5)(-5/sqrt21) = 2/sqrt21 = 2sqrt21/21`
`cot t = sqrt21/2`
`sec t = 5/sqrt21 = 5sqrt21/21`