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:

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

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

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