Copy and complete the following table of function values. If t...

Question

Copy and complete the following table of function values. If the function is undefined at a given angle, enter “UND.” Do not use a calculator or tables.

tab

Accepted Answer

Below there, today we're going to solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. Which of the following tables show correct trigontric function values? OK, so it appears for this particular prong, we're ultimately trying to figure out which of these 4 different tables, since we're given a table for A, B, C, and D, we're trying to figure out which of these tables show correct trigontric function values. That's what we're ultimately trying to solve for which of these 4 tables is the correct table. That correctly, I should say, represents the trigonometric function values. So with that said, to quickly summarize here, we have 4 different tables, and in at the top of our tables for the first row, represented in gray, we have different values for theta, the angle, and then going down. Our first column of our table, the far left, it says it's going to be different values for sin theta, cosine theta, and tangent of theta. And when you fill in the different values in the table, as you can see, each value for theta is different for each table and such is the same for sine, cosine, and tangent. So now that we know that we got 4 different tables with 4 different values for each of these different squares in our table, The first step that we need to take in order to help us solve this particular problem is we need to recall and use the unit circle. So you should have been introduced in your class or maybe run ran across a video here on Pearson. About the unit circle, but we're going to use the unit circle to help us solve for this particular problem. And as you can see, or as you should recall and remember, the unit circle is set up like a coordinate plane where the Y axis is our vertical axis and the X-axis is our horizontal axis, and the unit circle represents both all the units in degrees for the angle theta, and we also have it in radiance units too. And as you could see, if we were to use different values for the at the angle, which we have pi divided by 3, you could just find pi divided by 3 on our unit circle and use that to help us fill out our table, and that's how we're gonna approach and solve this particular problem. So let us also quickly recall right now that the cosine of the angle corresponds to the X coordinate of the points on the unit circle. So let's make a note of that. So, X, Y is our coordinate point. So let us note that X denotes our cosine value, whereas our Y value denotes the sign. So, on the other hand, the sign of the angle will correspond to the Y coordinate plane. So, so sine denotes our Y that's the point in our coordinate point, whereas cosine denotes X. So with that said, let us consider our table option for multiple choice answer A. And as you can see from the unit circle, sign, so if you go to, since we're saying our first angle, so theta equals pi divided by 3. So if we go to pi divided by 3 on our unit circle, we will see that sign of pi divided by 3 is going to be equal to square rooted 3 divided by 2. And looking at our table, it's saying that Sign of pi divided by 3 is equal to 12, which this will make it incorrect because as we determined, sign of pi divided by 3 gives us square root of 3 divided by 2. It is not one half. So it cannot be multiple choice answer letter A. So looking at multiple choice answer letter B, so from the unit circle, we're told that theta equals pi divided by 4. So if we look at pi divided by 4, we will find that Sine is equal to the square root of 2 divided by 2, and this does agree with the table. So let's check another value. So when sign equals 2 pi, so now we're looking for 2 pi divided by 3. So for 2 pi divided by 3, that means that sign is going to be equal to square root of 3 divided by 2. Which that also agrees with our table. So now we need to consider sign of 5 pi divided by 4. So if we look for 5 pi divided by 4, so let's look for 5 pi divided by 4, we will find that sign of 5 pi divided by 4 will give us negative square to 2 divided by 2. And this It will give us an incorrect value because on our table, we have a negative square or 2 divided by 2, and on the table for multiple choice B, it is not a negative value, so it cannot be multiple choice answer letter B. Moving right along here. So now looking at multiple choice answer letter C, we're told that theta is going to be equal to pi divided by 6. So if we look for pi divided by 6, we'll find that sin up pi divided by 6 is equal to 1/2. So that is true in our table and true with our unit circle. So now looking at our second value, which is 3 pi divided by 4. So if you look at sign of 3 pi divided by 4, so let's find 3 pi divided by 4. We'll find that it's equal to squared 2 divided by 2. And As you could see, Looking, all right, as we said 3 pi. So we're looking at 3 pi divided by 4, so 3 pi divided by 4, which will give us squared 2 divided by 2, but in our table for C, as we could see, it is a negative value, so that is not correct. So that means Without a doubt, it has to be multiple choice answer letter D, but just to be sure, let's quickly check our answer to make sure it's correct. So looking at D, let's try our first value for theta, which is 7 pi divided by 6. So if we look at 7 pi divided by 6 on our on our unit circle, we will find that it's going to be equal to -12, which confirms, which is confirmed in our table. So let's look at 7 pi divided by 4. So if you go look for 7 pi. Divided by 4, we will find that our sign value is gonna be is gonna be equal to negative, square rooted 2 divided by 2, which is confirmed by our table. And if we look for 11, Pi divided by 6, so 11 pi divided by 6, signs going to be -12, and that confirms with our table. So, once again, sign of 11 pi divided by 6 is going to be equal to -12, and this is confirmed on our unit circle and in our table. And that's it. We've officially solved for this problem. Hooray! Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Copy and complete the following table of function values. If the function is undefined at a given angle, enter “UND.” Do not use a calculator or tables.

Key Concepts

Function Values

Undefined Functions

Trigonometric Identities

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