Question

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

Answer 1

Answer: option a.

Step-by-step explanation:

By definition, we know that:

$cos^2(\theta)=1-sen^2(\theta)\\\\tan(\theta)=\frac{sin(\theta)}{cos(\theta)}$

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

$cos(\theta)=\±\sqrt{1-(\frac{6}{11})^2}\\\\cos(\theta)=\±\sqrt{\frac{85}{121}}\\\\ cos(\theta)=\±\frac{\sqrt{85}}{11}$

As $sec\theta$ then $cos\theta$:

$cos(\theta)=-\frac{\sqrt{85}}{11}$

Now we can find $tan\theta$:

$tan\theta=\frac{\frac{6}{11}}{-\frac{\sqrt{85}}{11}}\\\\tan\theta=-\frac{6\sqrt{85}}{85}$

Answer 2

Answer:

a

Step-by-step explanation: