Determine whether the positive or negative square root should ...

Question

Determine whether the positive or negative square root should be selected.

cos 58° = ±√ (1 + cos 116°)/2]

Accepted Answer

Hello, everyone which of the following expressions is equivalent to the cosine of 69 degrees. Our answer choices are a negative square root of the fraction one plus the cosine of 138 degrees divided by two B, the square root of the fraction one plus the cosine of 138 degrees. All of which divided by two C, the square root of the fraction one minus the cosine of 138 degrees divided by two D negative square root of the fraction one minus the cosine of 138 degrees divided by two. All right. First thing I want to look at these answer choices look very similar to our cosine half angle identities. So our cosine half angle identity says that the cosine of angle A divided by two is equal to plus or minus the square root of one plus the cosine of a divided by two. So I'm gonna work with this identity. First thing I need to figure out is what is a. So if the cosine of A divided by two is gonna equal the cosine of 69 degrees, we can say a divided by two equals 69 degrees. And to isolate A, we multiply both sides by two N A has equal 138 degrees. So next, I'm gonna place that into this formula. So I will have the cosine of 69 degrees equals and it is plus or minus. But since cosine is positive in quadrant one and 69 degrees would be in quadrant one, we are only gonna work with the positives. So we'll have the positive square root of one plus the cosine of a which we said was 138 degrees, all of which is divided by two. Since 138 degrees is not on our unit circle. It's not one of those exact measurements we're stopping here and this is our solution. The square root of the fraction one plus the cosine of 138 degrees divided by two which matches answer choice B have a nice day.

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Determine whether the positive or negative square root should be selected.
cos 58° = ±√ (1 + cos 116°)/2]