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.

-sin 35°

Accepted Answer

Hello, everyone. We are asked which of the following expressions is equivalent to the negative sign of 228 degrees. Our answer choices are A, the sign of negative 228 degrees B two sine of 456 degrees cosine of 456 degrees C cosine squared, 228 degrees minus the sine squared of 228 degrees D negative one divided by the C can of 228 degrees. So we have a lot of different identities. So let's go through our answer choices and see what fits for A, this looks like an odd even identity. And I recall that if I have this sign of negative X, this would be equal to the negative sine of X and that appears to be what we have here. So that works. But I wanna double check the rest of them. For answer choice B this appears to be similar to our double angle identity for sine which says the sine of two A equals two sine of a cosine of A. But for this to work, we would have to have the sine of two A equals the negative sign of 228. So two A would have to equal 228 degrees and A would have to be 114 degrees, not 456 degrees. So this does not work for C again, this looks like another double angle identity. So we have the cosine A two A what equal cosine squared of A minus sine squared of A. But again, for this to work, the cosine of two A would have to equal the negatives of 228 degrees. And those are different functions. So that just does not work. And then D I think D is working off the idea of a reciprocal identity but one divided by the C can of an angle is the cosine of that angle, not the sign. So D doesn't work either. So our answer choice A, the sign of negative 228 degrees is our answer. 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.
-sin 35°

Key Concepts

Trigonometric Identities

Negative Angle Identities

Angle Complement and Supplement Relationships

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