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Hi, can you help me to solve this exercise, please!

Hi, can you help me to solve this exercise, please!-example-1

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Question:

Solution:

By definition:


\sin ^2(\theta)+\cos ^2(\theta)=1

You can divide by cos² x:


\tan ^2(\theta)+1=\sec ^2(\theta)

now, solving for theta, we get:


\sec (\theta)=\pm\sqrt[]{tan^2(\theta)+1}

According to this and the data of the problem, this is equivalent to:


\sec (\theta)=\pm\sqrt[]{(12)/(11)}

Note that the minus sign is because the angle is in the third quadrant. So that, we can conclude that the correct answer is:


\sec (\theta)=-\sqrt[]{(12)/(11)}

Hi, can you help me to solve this exercise, please!-example-1
User Kevin Kalitowski
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