Find the values of the trigonmeric functions of t from the given information

Question

cos t = -4/5 terminal point of t is in quadrant III

Answer 1

First find the absolute values of each function, and assign the sign accordingly for quadrant 3.

The signs of the different functions are as follows:

S|A
---
T|C

which shows that in Quad 1, All trigonometric functions are positive, in Q2, only Sine and cosecant are positive. In Q3, Tangent and cotangent are positive. In Q4, Cosine and secant are positive.

cos(t)=-4/5,
sin(t)=√(1-(-4/5)²)
=3/5
The sign for sin(t) in quadrant 3 is -ve, so sin(t)=-3/5.
tan(t)=sin(t)/cos(t)=3/4
In Q3, tangents are positive, so tan(t)=3/4.

I'll leave it to you to figure out the remaining functions, namely cosecant, secant and cotangent.