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. a. arccos(1/2)

Accepted Answer

Welcome back, everyone. Determine the exact value of inverts of cosine of -12. A says pi divided by 3. B 2 divided by 3. C pi divided by 4, and D 5 pi divided by 6. For this problem we're looking for the principal value of an angle theta which is equal to inverse of cosine of -12. Let's remember that theta belongs to the interval from 0 to pi inclusive, right? And now, what we're going to do is simply take cosine of both sides, so that cosine of theta is going to be equal to -12. What we're going to do is identify the reference angle for positive 1/2. Let's remember that if cosine of alpha is equal to 1/2, then alpha is equal to pi divided by 3. This is one of the known values. Cosine of pi divided by 3 is 1/2. Now, cosine is negative in the second quadrant, so we're going to take quadrant number 2. And what we're going to do is identify the required angle theta using the reference angle formula, right? So theta is going to be equal to pi minus alpha, which is pi minus pi divided by 3, and this is equal to 2 pi divided by 3, meaning the correct answer for this problem corresponds to the answer choice B. Thank you for watching.

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

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