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 300°

Accepted Answer

Hello, everyone. We are asked which of the following expressions is equivalent to the sign of 328 degrees. Our answer choices are A, the sine of 300 degrees cosine 28 degrees minus the cosine of 300 degrees sine of 28 degrees B, the cosine of 300 degrees cosine of 28 degrees minus the sine of 300 degrees sine of 28 degrees C two multiplied by the sine of 164 degrees cosine of 164 degrees D. The sign of negative 328 degrees, we have many different angle identities. So let's see which one of these is a true angle. Identity that is equivalent to the sign of 328 degrees. Answer choice A looks a lot like if we had the sum of two angles. So the sign of a sum of two angles A plus B, but that identity states that it's the sign of A cosine of B plus the cosine of a sign of B so close. But the wrong signs in between for answer choice B, what this looks closest to is if we were looking at the sum of angles for a cosine. So if we had the cosine of the sum of A plus B, since we're looking for sign, this doesn't work because it's not the sign of A plus B for C. This looks like our S double angle formula or identity. So the sign of two A, what do you call two sign of a co sign of A? So for this to work 164 degrees times two or multiplied by two has to equal 328 degrees, which it does. So I think answer choice C is gonna be our answer. But let's look quick at answer. Choice D answer choice D is assuming this is an odd versus even function. And we didn't have a negative in our original. So we're not gonna have a negative in our answer. So answer choice C to sign of 164 degrees cosine of 164 degrees is the correct 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 300°

Key Concepts

Reference Angles and Quadrants

Trigonometric Identities

Unit Circle Values

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