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ludmilkaskok [199]
3 years ago
15

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

Mathematics
2 answers:
bekas [8.4K]3 years ago
4 0

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}

Brut [27]3 years ago
4 0

Answer:

a

Step-by-step explanation:

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