🎉 The Study-to-Win Winning Ticket number has been announced! Go to your Tickets dashboard to see if you won! 🎉View Winning Ticket

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 18

Evaluating Trigonometric Functions In Exercises $17-20$ , sketch a right triangle corresponding to the trigonometric function of the acute angle $\theta$ . Then evaluate the other five trigonometric functions of $\theta$.

$$\sin \theta=\frac{1}{3}$$

Answer

(ANSWER NOT AVAILABLE)

You must be logged in to bookmark a video.

...and 1,000,000 more!

OR

## Discussion

## Video Transcript

all right. So question Number 18 asks us to sketch a right angled triangle corresponding to the Trigana metric function of the acute angle data. Then evaluate the other five children a metric functions of data. So let's start by sketching that right triangle. Put that right there to indicate it's 90 degrees. Then I want to say that it is up here. Now when we look at this expression we've been given, synthetic was 1/3. We know that this 1/3 is a ratio of side lengths. So for sign, that's going to be the opposite. Sign the side opposite our angle over the high pot news. Okay, Now, if we want aside this up, if we want to find this other side be, let's say we're gonna have to do the Pythagorean theorem, which is a squared plus B squared equals C squared where this side of sea and this side is Hey, so we have one. Let's be squared equals three squared, which is nine. So I have B squared equals nine minus one, which is eight b equals the square root of a which can be simplified, but we got to 4 to 2 just seeing what we can factor out. We can fact around it to. Which leaves us with two square root too. As this side over here being now that we have found all three sides, we can easily express the other five. You're gonna metric functions of this acute angle theta as this ratios between these sides so well say co sign Fada equals tangent, data equals and we'll have seeking Veda equals co seeking theta equals tangent. Data equals Let's put our answers in green. So the coastline of the single is simply gonna be the adjacent sign over the high pot News or two square root to over three tangent is gonna be the opposite side over the adjacent side of that angle. One over two square two Now seek in. It's simply going to be the reciprocal of coastline. So we'll have three over two square two Coast seeking will be the reciprocal of Sign A three and then co tangent will be the reciprocal A tangent. A two square root too. And there you have it. These are the five other triggered a metric functions for the acute angle data

## Recommended Questions

Evaluating Trigonometric Functions In Exercises $17-20$ , sketch a right triangle corresponding to the trigonometric function of the acute angle $\theta$ . Then evaluate the other five trigonometric functions of $\theta$.

$$\sec \theta=\frac{13}{5}$$

Evaluating Trigonometric Functions In Exercises $17-20$ , sketch a right triangle corresponding to the trigonometric function of the acute angle $\theta$ . Then evaluate the other five trigonometric functions of $\theta$ .

$$\sin \theta=\frac{1}{2}$$

Evaluating Trigonometric Functions In Exercises $17-20$ , sketch a right triangle corresponding to the trigonometric function of the acute angle $\theta$ . Then evaluate the other five trigonometric functions of $\theta$.

$$\cos \theta=\frac{4}{5}$$

In Exercises 13-20, sketch a right triangle corresponding to the trigonometric function of the acute angle $\theta$. Use the Pythagorean Theorem to determine the third side and then find the other five trigonometric functions of $\theta$.

sec $\theta = \frac{17}{7}$

In Exercises 13-20, sketch a right triangle corresponding to the trigonometric function of the acute angle $\theta$. Use the Pythagorean Theorem to determine the third side and then find the other five trigonometric functions of $\theta$.

sin $\theta = \frac{1}{5}$

In Exercises 13-20, sketch a right triangle corresponding to the trigonometric function of the acute angle $\theta$. Use the Pythagorean Theorem to determine the third side and then find the other five trigonometric functions of $\theta$.

tan $\theta = \frac{3}{4}$

tan $\theta = \frac{4}{5}$

cot $\theta = 3$

Sketch a right triangle corresponding to the trigonometric function of the acute angle $\theta .$ Use the Pythagorean Theorem to determine the third side of the triangle and then find the values of the other five trigonometric functions of $\theta$. $$\csc \theta=\frac{17}{4}$$

sec $\theta = \frac{3}{2}$