In Exercises 2332 find the values of the six trigonometric f

In Exercises 23-32, find the values of the six trigonometric functions of theta with the given constraint. Function value Constraint tan theta = -15/8 sin theta > 0 cos theta = 8/17 tan theta 0 csc theta = 4 cos theta

Solution

28. csc theta=4    and cot theta<0

It means sin theta is positive and cos theta is negative

sin theta=1/csc theta=1/4

Here opposite=1   and   hypotenuse=4

adjacent=sqrt(16-1)=sqrt15

cos theta= -sqrt15/4

tan theta= sin theta/cos theta= -1/sqrt15= -sqrt15/15

cot theta=1/tan theta= -sqrt15

sec theta=1/cos theta= -4sqrt15/15