In Exercises 1–10, use substitution to determine whether the give...

Question

In Exercises 1–10, use substitution to determine whether the given x-value is a solution of the equation.
               
                    1               2𝝅
cos x = ﹣ ------- , x = ---------
                    2                 3

Accepted Answer

Hello everybody. I hope you're doing. All right. Today, today we're going to be looking at this question that states for the following trigonometric equation perform substitution to identify which of the following angles is a solution where our trigonometric equation is cosine of X is equal to negative square root of two divided by two. Now the answer choices provided are a five pi divided by six B two pi divided by three, C five pi divided by four and D four pi divided by three. Now how we're going to be tackling this question? We're going to be either using our calculator or recalling from the unit circle. No, to use substitution. What we're basically going to do is just do trial and error with the answer choices provided, plug those into our X in our equation and see if they work. So let's start with answer choice. A. If we plug in answer choice A to our equation, we'll have cosine of five pie divided by six. And we can either use our calculator or recall from the unit circle that this will give us negative square root of three divided by two, which is not the answer that we are looking for. So we will move on to answer choice B. If we plug in as choice B, we'll have cosine of two pi divided by three. And once again, either using the calculator or recalling from the unit circle, this will give us an answer of negative one half, which is not what we are looking for. So we move on to answer choice C and then we plug in as choice C. We'll have cosine of five pi divided by four, which is equal to using the calculator or unit circle, negative square root of two divided by two, which is the answer we are looking for. But we can move on to answer choice D just to confirm and we plug an extra choice D to have cosine of a four pi divided by three which is equal to negative one half, which is not what we are looking for. And we can confirm that answer. Choice C gives us the correct answer for this question. So you can see how important it is to be able to recall unit circle values, let's say in a test where maybe you're not allowed to use a calculator, you have to be able to recall these values. And especially if it's timed. If you can just recall, you will be able to solve these much quicker. So I hope that was helpful. And until next time

In Exercises 1–10, use substitution to determine whether the given x-value is a solution of the equation. 1 2𝝅 cos x = ﹣ ------- , x = --------- 2 3

Key Concepts

Cosine Function

Substitution Method

Radian Measure

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