Use the function given to determine the value of the other f

Use the function given to determine the value of the other five trig functions of the acute angle theta. Answer in exact form (a diagram will help). Tan theta <0 and cos(theta)= 5/8

PLEASE SHOW WORK!

Solution

cos theta = 5/8

Tan theta is negative in second and fourth quadrant. But in second quadrant cos theta is negative too. And here cos theta is positive. Hence theta is in fourth quadrant

adjacent =5    and hypotenuse =8

opposite =sqrt(64-25) = sqrt 39

sin theta = opposite/hypotenuse =-sqrt39/8

tan theta= sin theta/cos theta= -sqrt39/5

sec theta= 1/cos theta = 8/5

csc theta=1/sin theta =- 8/sqrt39 = -8sqrt39/39

cot theta = 1/tan theta = -5/sqrt39 =-5sqrt39/39