Use the given information to find the exact values of the five remaining trigonometric functions of Ø

Question

1. Tan Ø = -21/20

Sin Ø < 0

2. Sec Ø = -√10

Cot Ø > 0

Answer 1

First, we must determine what quadrant ø is in. We know that tangent is negative in QII & QIV. We also know that sine is negative in QIII & QIV. This shows that in order for the sine of ø and tangent of ø to both be negative, ø must be in QIV. If we make a right triangle with -21 on the opposite side of ø and +20 on the adjacent side, we can find that the hypotenuse is hyp. = √(-21)² + (20)²--->hyp. = 29.

sinø = opp./hyp.

cosø = adj./hyp.

tanø = opp./adj.

cscø = hyp./opp.

secø = hyp./adj.

cotø = adj./opp.

I'll leave the rest for you.

Hope this helps!