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.
               __
             √ 2              𝝅
cos x = ------- , x = ------
               2               4

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. Now, our trigonometric equation is cosine of X is equal to the square root of three divided by two. Now the answer choices provided are a pi divided by six B pi divided by three C P divided by four and D pi divided by two. Now to tackle this question, we are going to be either using our calculator four, recalling from the unit circle, we can use either method I suggest being able to recall so you can know these values right away and I'll explain why need more at the end. Now to do substitution, all we're going to be basically doing is just trial and error with our answer choices, plugging each one into our equation and see which one works. So we'll start with answer choice. A. If we plug in pi divided by six into our X, we'll have cosine of pi divided by six and using our calculator or recall, we know that cosine of pi divided by six is positive squared of three divided by two, which is the answer that we're looking for. Now, we're going to try BC and D just to confirm that this is correct. So for answer choice B, we'll plug it into our equation and we'll have cosine of pi divided by three using the calculator or recall. We know that this is one half which is not what we are looking for. And we move on to answer choice C where once we plug it in, we'll have cosine of pi divided by four which using our calculator or recalling will have that this is equal to positive squared of two divided by two, which is not what we are looking for. And we move on to answer choice D which once we plug that in will be cosine of pi divided by two. And once again using the calculator or recall, we know that cosine of pi divided by two is equal to zero, which is not what we are looking for. And we have confirmed that answer choice A is the correct answer for this question. Now, it is very important to be able to recall these values from the unit circle right away because let's say you're not allowed to use a calculator during a test, you need to be able to recall the values, especially if it's a timed test. If you are able to just recall these values, you would be able to solve these questions much quicker and save yourself a lot of time. 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. __ √ 2 𝝅 cos x = ------- , x = ------ 2 4

Key Concepts

Cosine Function

Substitution Method

Radian Measure

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