University of Southern California

Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
Problem 58
Problem 59
Problem 60
Problem 61
Problem 62
Problem 63
Problem 64
Problem 65
Problem 66
Problem 67
Problem 68
Problem 69
Problem 70
Problem 71
Problem 72
Problem 73
Problem 74
Problem 75
Problem 76
Problem 77
Problem 78
Problem 79
Problem 80

Problem 22

Evaluating Trigonometric Functions In Exerrises $21-24$ , evaluate the sine, cosine, and tangent of each angle. Do not use a calculator.

$$\begin{array}{lll}{(a)-30^{\circ}} & {\text { (b) } 150^{\circ}} & {\text { (c) }-\frac{\pi}{6}} & {\text { (d) } \frac{\pi}{2}}\end{array}$$

Answer

See Solution

You must be logged in to like a video.

You must be logged in to bookmark a video.

## Discussion

## Video Transcript

all right. Problem Number 22 asks us to evaluate the sign co sign in tangent of each of the following angles. And the one caveat is we're not allowed to use our calculator. So how are we going to do this? Well, we're gonna use the unit circle now. The unit circle has a select or a few key angles that have really nice, um, defined values for coastline and sign. So the first thing we're gonna look at is negative 30 degrees. I'm gonna come into our unit circle. We know that this horizontal line on the right in deposit direction corresponds to zero degrees. So negative 30 degrees is just down like that. And something that's unique about this, um, negative 30 degrees is that the coastline value is equal to square root three over two, and then the sign value is equal to negative 1/2. And that's just a property of the unit circle that over time you will memorize. And so because we know that it becomes fairly easy to evaluate sine, cosine and tangent co sign of negative 30 degrees is going to equal that X value writes. How much is in this direction. And so that equals square it. Three over two. Sign of negative. 30 equals negative 1/2. And then tangent of negative 30 is the same as the sine divided by the coastline. So you can see. Yeah, my device were three over two. These twos cancel out on your left. Negative one over. Square root three. So that bray or for letter A now for part B were given a value of 115. Well, we can think of that. As is This whole isn't. I need this quadrant here is 90 degrees plus nineties. 1 80 minus 30 is gonna equal 1 50 And so right here, we'll find ourselves at 130 degrees because it is a multiple of 30 degrees. We have it as Ah, it's one of those unique values, right? And so the X right here he's going to equal square it. Three over two and the wife was 1/2. And so we go back. Family can do the exact same process again. Co sign of 150 degrees is equal to. That's a negative because of the negative direction is equal to negative square three over two. Sign of 150 degrees sequel, The positive 1/2 and then for a tangent of 150 degrees. We have 1/2 divided by negative square three over two, and that's going to equal one or square three wrote that kind of funky one negative one over square three. All right, so that's the answer. Be See is our first angle and radiance And one thing that we will are you should realize is that negative pie six is equivalent to negative 30 degrees If you're to use that conversion factor for that where you go negative pie six times two pi over 360. You'd soon see to this just equals negative 30 degrees, Which means heart am part See, have the exact same answers So same and then over for being was gonna circle answers right now just cause things look like they're getting kind of messy. And I don't want you guys to get lost now for D We come in here and were given pie halfs soap. I half is a really nice one. It's just right here by half also equals 90 degrees and a pie Halfs X equals zero, right? It was one So our co sign of Pi House equal zero. Our sign of pie halfs equals one. And then our tangent of perhaps which is just the sign over coastline goes one over zero mats undefined. So that doesn't really exist. There you have it because you can't divide, you know, one by zero. And they have it. Those for the sign coast and tangents for each of the four angles listed above.

## Recommended Questions