Write each function in terms of its cofunction. Assume all angles...

Question

Write each function in terms of its cofunction. Assume all angles involved are acute angles. See Example 2.

cos(θ + 20°)

Accepted Answer

Welcome back everyone. In this problem, we want to write the cosine of alpha plus 31 degrees in terms of its core function. For our answer choices. A says the core sign of 59 degrees minus alpha B is the sign of 59 degrees minus alpha C is the sign of 59 degrees plus alpha and D is the sign of alpha plus 31 degrees. Now, what do we already know? Well, recall that when we're talking about the core function, recall that the core sign of theater is equivalent to the sign of 90 minus theater degrees for an acute angle of theater. In other words, the core function values of complementary angles are equal. So if we know the value of our angle in the cosine function, we should be able to substitute it to solve for our known value for the sine function. No, notice that our angle here is alpha plus 31. So since our angle is alpha plus degrees, we can substitute it to solve for our core function sine value. Because now that tells us then that the cores sign of this angle alpha plus 31 degrees will be equivalent to the sine of 90 minus that angle. So 90 minus alpha plus 31 degrees. Now, when we simplify it, that would be equal to 90 minus alpha minus 31 degrees. And no notice that we have two like terms minus 31 degrees, which equals 59 degrees. So that would be the sign of 59 degrees minus alpha. Therefore, the cosine of alpha plus 31 degrees is equivalent to the sign of 59 degrees minus alpha for its core function. When we look in our answer choices that would have been answer choice. B thanks a lot for watching everyone. I hope this video helped.

Write each function in terms of its cofunction. Assume all angles involved are acute angles. See Example 2. cos(θ + 20°)

Key Concepts

Cofunction Identities

Angle Addition Formulas

Acute Angles

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