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.
               __
             √ 3              𝝅
sin x = ------- , x = -------
               2               6

Accepted Answer

Hello everybody. I hope you are 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 sign of X is equal to the square root of two divided by two. Now the answer choices provided are a pi divided by six B pi divided by three C pi divided by four and D pi divided by two. Now to tackle this question, we can go two routes. We can either be using a calculator four. Recall from the unit circle. I suggest you use your unit circle. These are values that you should be able to recall right away. Now to perform substitution. What we're going to be basically doing is just try and error with our s choices. We're going to be plugging each one into our equation and see which one works. So let's start with answer choice. A. If we plug in answer choice A, we'll have a sign of pi divided by six and using a calculator or recalling from the unit circle, we know that sign of pi divided by six is equal to one half, which is not the answer that we're looking for. So we move on to answer choice B, every plug-in answer choice B will have sign of pi divided by three. And once again using the calculator or recalling from the unit circle, this will give us the square root of three divided by two, which is not the answer that we are looking for. So we move on to answer choice C. If we plug in as a choice C, we'll have a sign of pi divided by four, which is equal to, if we use a calculator or recall, this will give us positive square root of two divided by two, which is the answer we're looking for. But we'll try answer choice D just to confirm that C is the correct one. So if we plug an answer, choice D, we'll have sign of pi divided by two. And now once again, using the calculator or recalling this will give us positive one, which is not the answer that we are looking for. And we can confirm that answer. Choice C is the correct answer for this question. Now, this teaches us how important it is to be able to recall the unit circle values and know how to use them properly. Let's say in a test, you're not allowed to use a calculator, you have to be able to recall those values from the unit circle. And especially if a test is timed. If you can just recall right away, you will be able to solve questions like this much faster. 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. __ √ 3 𝝅 sin x = ------- , x = ------- 2 6

Key Concepts

Trigonometric Functions

Substitution Method

Radians and Degrees

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