Question:
Solution:
By definition:
[tex]\sin ^2(\theta)+\cos ^2(\theta)=1[/tex]
You can divide by cos² x:
[tex]\tan ^2(\theta)+1=\sec ^2(\theta)[/tex]
now, solving for theta, we get:
[tex]\sec (\theta)=\pm\sqrt[]{tan^2(\theta)+1}[/tex]
According to this and the data of the problem, this is equivalent to:
[tex]\sec (\theta)=\pm\sqrt[]{\frac{12}{11}}[/tex]
Note that the minus sign is because the angle is in the third quadrant. So that, we can conclude that the correct answer is:
[tex]\sec (\theta)=-\sqrt[]{\frac{12}{11}}[/tex]
