Question

find the exact value of each of the remaining trigonometric functions of theta sec(theta)=-8, sin(theta)>0

Answer 1

magic

Answer 2

\[\sec(\theta) = -8\]

Answer 3

recall that
\[\sec(\theta) = \frac {1}{\cos(\theta)}\]

Answer 4

so,
\[\frac {1}{\cos(\theta)} = -8 \rightarrow \frac {1}{-8} = \cos(\theta) \rightarrow \cos^{-1}(\frac{1}{-8}) = \theta\]