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

Question

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

sin (-10°) = ± √[(1 - cos (-20°))/2]

Accepted Answer

Hello, everyone. We are asked which of the following expressions is equivalent to the sign of negative 27 degrees. Our answer choices are a, the square root of the fraction one minus the cosine of 54 degrees divided by two B, the square root of the fraction one plus the cosine of 54 degrees divided by two. See the negative square root of the fraction one minus the cosine of 54 degrees divided by two D, the negative square root of the fraction one plus the cosine of 54 degrees divided by two. So first, I recall that due to odd and even identities that if I have the sign of a negative angle like negative X, it will equal the negative sign of X. So using this idea, the sign of negative 27 degrees will be equivalent to the negative sign of 27 degrees. So I'm gonna keep that in mind going forward. Next, our answer choices look similar to our half angle identities. So since we're working with sign, I want to compare them to the sign half angle identities. And I find that the sign of a divided by two as equal plus or minus the square root of one minus the cosine of a, all of which divided by two. So if this is the case, we can say that we are working with the sign of A, divided by two has to be equal to the sine of 27 degrees. A divided by two would have to equal 27 degrees. Multiplying both sides by two to isolate the A I get that A would be 54 degrees. So I'm gonna use that in my formula. So I'm gonna say the sign of 27 degrees equals and since 27 is in quadrant one, we're gonna deal with the positive square root of one minus the cosine of 54 degrees divided by two. Now, since 54 degrees does not have the ability to be used on a unit circle. There's not much else we can do here. However, we are supposed to be working with the negative sign of 27 degrees. So that means we need to negate both sides. So we'll have the sign of or sorry, the negative sign of 27 degrees. And this is going to equal the negative square root of one minus the cosine of 54 degrees divided by two. So this is our answer the negative square root of the fraction one minus the cosine of 54 degrees divided by two, which is answer choice C have a nice day.

Struggling with Trigonometry?

Determine whether the positive or negative square root should be selected.
sin (-10°) = ± √[(1 - cos (-20°))/2]

Watch next

Double Angle Identities practice set

Struggling with Trigonometry?

Determine whether the positive or negative square root should be selected.sin (-10°) = ± √[(1 - cos (-20°))/2]

Watch next

Double Angle Identities practice set

Determine whether the positive or negative square root should be selected.
sin (-10°) = ± √[(1 - cos (-20°))/2]