For each expression in Column I, use an identity to choose an ...

Question

For each expression in Column I, use an identity to choose an expression from Column II with the same value. Choices may be used once, more than once, or not at all.

cos(-55°)

Accepted Answer

Hello, everyone. We are asked which of the following expressions is equivalent to the cosine of negative 92 degrees. Our answer choices are A, the cosine of 92 degrees B, the negative cosine of 92 degrees C one plus two sine squared of negative 46 degrees D two cosine squared, negative 46 degrees plus one. So I know we have a lot of identities. So let's see which ones apply here. Looking at answer choice. A answer choice A would work as long as our odd even functions. Tell us that the cosine of negative theta is equal to the cosine of theta. And it does. So answer choice A definitely works. Let's verify the rest just in case for answer choice B, this is the wrong odd and even function. We just said that the cosine of negative theta equals the cosine of theta. So answer choice B doesn't work because we wouldn't have negative cosine of 92 degrees. Answer choice C is assuming we have a double angle which would be fine. Let's see our double angle identity. This one would be the cosine of two. A after equal one minus two sine squared of A, we have the wrong sign in between our terms. So it's not C answer choice D is looking at a different double angle identity where the cosine of two A would equal two cosine squared A minus one. And again, we have the wrong sign. We have a plus one in that answer choice. So this means answer choice. A, the cosine of 92 degrees is the equivalent expression. Have a nice day.

For each expression in Column I, use an identity to choose an expression from Column II with the same value. Choices may be used once, more than once, or not at all.
cos(-55°)

Key Concepts

Even-Odd Identities

Trigonometric Values of Common Angles

Trigonometric Identities

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