Exact Values with Trigonometric Functions

Question

Given that csc theta = 5/2 and tan theta<0. FInd the remaining five trigonometric function value of theta. Give Exact Values.

Answer 1

The given cosecant value tells you that sine θ = 2/5 and the fact that tangent is negative places the angle θ in quadrant II, where sines are positive but cosines are negative.

 

cos θ  must be -√21/5 using the Pythagorean identity.

 

From these facts you can easily finish the job.