Use reference triangles in an appropriate quadrant to find the...

Question

Use reference triangles in an appropriate quadrant to find the angles in Exercises 1–8.

5. c. arccos(√3/2)

Accepted Answer

Welcome back, everyone. Determine the exact value of inverse of cosine of negative square root of 3 divided by 2. A says pi divided by 6. B pi divided by 3. C 7 pi divided by 6, and D 5 pi divided by 6. For this problem we're looking for the angle theta such that theta is equal to inverse of cosine of negative square root of 3 divided by 2. Let's remember that the range of theta belongs to the interval from 0 to pi inclusive. Notice that if we take cosine of both sides, then cosine of data is going to be equal to square root of 3 divided by 2, and that essentially means that our angle is in quadrant number 2 because this is where cosine is negative, right? Considering the range from 0 to pi inclusive, what we're going to do is use reference angles. So we're going to take an angle alpha such that cosine is positive. We're going to take cosine of alpha equals square root of 3 divided by 2, and remember that this is a perfect angle, right? Alpha is going to be equal to pi divided by 6. Because cosine of pi divided by 6 gives us square root of 3 divided by 2. So now considering quadron 2, we can identify theta using the reference angle formula. Theta is equal to pi minus alpha, which is pi minus pi divided by 6, which is equal to 5 divided by 6. And this corresponds to the answer choice D. Thank you for watching.

Use reference triangles in an appropriate quadrant to find the angles in Exercises 1–8.5. c. arccos(√3/2)

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Use reference triangles in an appropriate quadrant to find the angles in Exercises 1–8.
5. c. arccos(√3/2)