Question

Function value: csc theta = 4
Constraint: sin theta < 0
Find tan theta.

Is it -((sqrt15)/15)?

Answer 1

\[\sin ~ and~ \csc ~have~same~sign.\]
\[\csc ^2 \theta-\cot ^2 \theta=1\]
\[4^2-\cot ^2\theta=1\]
\[\cot ^2\theta=16-1=15\]
\[\tan ^2\theta=\frac{ 1 }{ 15 }\]
\[\sin \theta <0,means ~\theta~lies ~\in~3rd~or~4th~quadrant.\]
if in 3rd quadrant tan theta is positive
If in 4th quadrant tan theta is negative.