Write each function value in terms of the cofunction of a comp...

Question

Write each function value in terms of the cofunction of a complementary angle.

tan 174° 03'

Accepted Answer

Welcome back. Everyone. In this problem, we want to figure out which of the following core functions has the same value as the tangent of 167 degrees and 12 minutes. For our answer choices A says it's the tangent of 77 degrees and 12 minutes. B, the tangent of negative 77 degrees, 12 minutes C, the core tangent of 77 degrees 12 minutes and D the core tangent of negative 77 degrees 12 minutes. Now we're trying to figure out the core function with the same value as the tangent of our angle here 167 degrees, 12 minutes. What do we know about the core function? Well, we know that the core function is a way to relate trigonometric identities. So what do we know about the tangent? Well, recall that the tangent is complementary to the core tangent. That's its core function identity. In other words, the tangent of an angle is going to be equal to the core tangent of 90 degrees minus that angle, both of their angles should sum to 90 degrees. So since we know that an for are tangent here, we can substitute it in our core function identity to solve for the value of the core tangent. Because that now means that the tangent of 167 degrees 12 minutes is going to be equal to the core tangent of 90 degrees minus 167 degrees. 12 minutes. Now, 90 degrees minus 167 degrees, 12 minutes equals negative 77 degrees 12 minutes. Therefore, the core function that has the same value as the tangent of 167 degrees. 12 minutes is going to be equal to the core tangent of negative 77 degrees 12 minutes. D is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

Write each function value in terms of the cofunction of a complementary angle.
tan 174° 03'

Key Concepts

Complementary Angles

Cofunction Identities

Angle Conversion and Notation

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