Question

Given sin theta= 6/11 and sec theta < 0, find cos theta and tan theta.

Answer 1

a

Explanation:

Answer 2

Answer: option a.

Explanation:

By definition, we know that:

`cos^2(\theta)=1-sen^2(\theta)\\\\tan(\theta)=(sin(\theta))/(cos(\theta))`

Substitute
`sin(\theta)=(6)/(11)` into the first equation, solve for the cosine and simplify. Then, you obtain:

`cos(\theta)=\±\sqrt{1-((6)/(11))^2}\\\\cos(\theta)=\±\sqrt{(85)/(121)}\\\\ cos(\theta)=\±(√(85))/(11)`

As
`sec\theta<0` then
`cos\theta<0`:

`cos(\theta)=-(√(85))/(11)`

Now we can find
`tan\theta`:

`tan\theta=((6)/(11))/(-(√(85))/(11))\\\\tan\theta=-(6√(85))/(85)`