Question

PLEASE EXPLAIN STEP BY STEP find the remaining 5 trig functions when sec(theta)=-2 and cot(theta)>0

Answer 1

if cos is negative and cot is positive, then sin is ?

Answer 2

negative.

Answer 3

but how do i find the other five functions with the info given?

Answer 4

cool so since cos is neg and sin is neg
then we are in the third quadrant

Answer 5

we will build a triangle there

Answer 6

use that sec(theta)=-2 to label the triangle

Answer 7

sec(theta)=hyp/adj =2/(-1)

Answer 8

you will need to find the opp side measurement by use of Pythagorean theorem

Answer 9

then the rest is just
using the definition of the trig functions

Answer 10

\[\sin(\theta)=\frac{opp}{hyp} \\ \cos(\theta)=\frac{adj}{hyp} \\ \tan(\theta)=\frac{opp}{adj} \\ \csc(\theta)=\frac{hyp}{opp} \\ \sec(\theta)=\frac{hyp}{adj} \\ \cot(\theta)=\frac{adj}{opp}\]