Question

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

Answer 1

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)}`