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

Question

In Exercises 1–26, find the exact value of each expression._cos⁻¹ √3/2

Accepted Answer

Hello everybody. I have everything right today. Today we're going to begin this question as stage for the following trigonometric expression, evaluate and give the answer as an exact value in radiance where our expression is cosine to the exponent negative one of the screw of two divided by two. So this is inverse cosine. Now the answers provided are a pi divided by two B pi divided by three C pi divided by four and D pi divided by six. Now for a question like this, let's have an if and then situation. So let's say if the inverse cosine of squared of two divided by two is equal to X, then the normal cosine of X is equal to the squared of two divided by two. And this is how we can switch between inverse cosine and regular cosine. Now let's recall from the unit circle or before we do that, let's um talk about the range of inverse cosine. So cosine or inverse cosine is defined for a range of from zero to pi open bracket, zero comma pie closed bracket. So we are going to be in quadrant one. Why? Because cosine is positive in this case. So let's recall from the unit circle now and it's very important to know our unit circle values and being able to recall them at any moment's notice. Because for a question like this, we can recall right away that cosine of pi divided by four or before we address the actual cosine. Let's think of the point at pi divided by four. If we look at our unit circle, pi divided by four has a point at squared of two divided by two comma squared of two divided by two. Now, if X is equal to cosine theta and this is a fact in the unit circle, then cosine of pi divided by four is equal to the X component of pi divided by four. And if we look at the X component, it is squared of two divided by two. Therefore, the X in our question is equal to pi divided by four. And that would be the answer to our question which matches with answer choice C so you can see how valuable the unit circle comes in trigonometry, especially for questions like this one where we have to figure out the value of the specific angle. So we must memorize all of our unit circle values to be able to recall them at any moment's notice. So I hope that was helpful. And until next time

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In Exercises 1–26, find the exact value of each expression._cos⁻¹ √3/2

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