Find the exact value of tan(cos^-1(-12/13))

We could have just used the calculator to solve this problem, but to illustrate the concept we will use trigonometry. Let's break the problem first. 

Let A = cos^-1(-12/13) = arccos(-12/13)

So the problem now is searching for the exact value of tan(A).

A is an angle whose cosine is -12/13. Also, sin(A) using the pythagorean identity can be either positive or negative sqrt(1-(-12/13)^2) = +-5/13. But the arccosine gives angles in the range of 0 deg to 180 deg, so the only possible value for sin(A) is 5/13.

Using the quotient identities, tan(A) = sin(A) / cos(A) = 5/13 / (-12/13) = -5/12.

I hope my answer has come to your help. Thank you for posting your question here in . We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

62926281916 inches of rain: )