Question

If tan (theta) =5/4 and cos (theta) < 0 . Find the other trig. functions.

Answer 1

Tan(theta) = 5/4
sin(theta)/cos (theta)=5/4
cos(theta)=4sin(theta)/5
sin²(theta)+cos²(theta)=1
sin²(theta)+16sin²(iheta)/25=1  /*25
25 sin²(theta)+16 sin²(theta)=25
sin²(theta)=25/41    /√
sin(theta)=$\frac{-5 \sqrt{41} }{41}$
cos(theta)=$\frac{-4 \sqrt{41} }{41}$
cot(theta)=$\frac{4}{5}$
csc(theta)=1/sin(theta)=$\frac{- \sqrt{41} }{5}$
sec(theta)=1/cos(theta)=$\frac{- \sqrt{41} }{4}$