In Exercises 1–26, find the exact value of each expression.
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cos...

Question

In Exercises 1–26, find the exact value of each expression.
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cos⁻¹ (- √2/2)

Accepted Answer

Hello everybody. Uh We're doing all right today that we're going to be looking at this question that states for the following trigger amount of expression evaluate and give the answer as an exact value in radiance where the expression is co inverse cosine of negative one half. And the two are provided are a two pi divided by three B, three pi divided by four C five pi divided by four and D pi divided by six. Now, for this question, let's say if the inverse cosine of negative one half as he goes to a then cosine of X is equal to negative one half. And that's how we can switch from inverse cosine to regular cosine. Now let's recall and this is recalling values from the unit circle and just values that we should know in general, we should recall that cosine of pi divided by three is equal to positive one half. And we should also know a rule that cosine of open parentheses pi minus beta is equal to negative cosine of beta. So why is this important? We see that cosine of pi divided by three is equal to one half. Now, what wheat wants is negative one half. So if we can get negative cosine of pi over three or pi divided by three, then we will get negative one half. So let's rewrite our expression co sign. Now we now have cosine of open parentheses. Pi minus pi divided by three closed parentheses. And that will be equal to cosine of open parentheses. Three pi divided by three minus pi divided by three close parentheses. And this will be equal to cosine of two pi divided by three. So therefore, we have that cosine of two pi divided by three is equal to negative cosine of pi divided by three, which is equal to a negative one half. And this means that cosine or inverse cosine of negative one half is equal to pi divided by three. And that would be the answer to our question or it would be uh two pi divided by three. Actually, that's what, what the, the two pi divided by three is the one we calculated. So we have that the inverse cosine of negative one half is equal to two pi divided by three which matches with answer choice. A so we can see how important it is to be able to recall different values of the unit circle as well as being able to re have different ways of rewriting our expression that will help us later on. So I hope that was helpful. And until next time

In Exercises 1–26, find the exact value of each expression. _ cos⁻¹ (- √2/2)

Key Concepts

Inverse Trigonometric Functions

Unit Circle

Quadrants and Angle Values

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