Which one of the following equations has solution π?
a. ...

Question

Which one of the following equations has solution π?

a. arccos (―1) = x

b. arccos 1 = x

c. arcsin (―1) = x

Accepted Answer

Identify the equation which has a solution equals five pi divided by six where we have four possible answers. X equals cosine inverse negative scores to three divided by two X equals co in verse. Now of one half, X equals 10 inverse of one or X equals five inverse of negative one half. I've also put a unit circle on the right or our angle. Now our angle is that by pi divided by six, if we look at our unit circle, that engle is in quadrant two, now let's rewrite all of our answers. So we can use it with our unit circle. We can rewrite our answers by moving the cosine, for example, to the other side. OK, cosine X equals the square root of three divided by two. And that is negative. We'll do the same for all of our answers. Cosine X equals negative one F tangent X equals one and sin X equals negative one half. No, let's look at our angle. Again, we have X equals negative squared of three divided by two and Y equals one half at the angle five pi divided by six. We also know on the unit circle cosine corresponds to our X in sign corresponds to our Y. Now let's see if any of these match we have cosine X equals negative square roots of three divided by two. For the X that we notice our very first answer was changed to be cosine X equals negative squared of three divided by two. That means the answer to our problem is answer a cosine inverse negative squares of three divided by two. OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

Which one of the following equations has solution π?
a. arccos (―1) = x
b. arccos 1 = x
c. arcsin (―1) = x

Key Concepts

Inverse Trigonometric Functions

Values of Inverse Functions

Trigonometric Identities

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