Question

if sin(θ) = − 7/10 and sec(θ) >0, find the exact values of each of the trig functions

how would you work this out? could someone please explain?

cos(θ) =
tan(θ) =

cot(θ) =
sec(θ) =
csc(θ) =

Answer 1

Solve for \(\cos(\theta)\)
\[
\cos ^2(\theta )=1-\sin^2(\theta
)=1-\left(-\frac{7}{10}\right)^2=\frac{51}{100}\\
\cos(\theta)=\pm \frac{\sqrt{51}}{10}\\
\Large \cos(\theta)= \frac{\sqrt{51}}{10}\\Since\\
\sec(\theta)>0
\]

Answer 2

\[
\tan (\theta )=\frac{\sin
(\theta )}{\cos (\theta
)}=-\frac{7}{\frac{10
\sqrt{51}}{10}}=-\frac{7}{\sqrt{51}}\\
\cot(\theta)=-\frac{\sqrt{51}}7

\]

Answer 3

\[

\Large \sec(\theta)= \frac{10}{\sqrt{51}}\\Since\\

\csc(\theta)=-\frac{10}7
\]

Answer 4

thankyou so much for helping me again!