Q. 17 In Problems 16鈥�23, find the ex... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 6: Q. 17 (page 435)

In Problems 16鈥�23, find the exact value of each of the remaining trigonometric functions.
$\tan 胃 = \frac{12}{5}, \sin 胃 < 0$ .

Short Answer

Expert verified

The exact value of the remaining trigonometric functions for the given expression $\tan 胃 = \frac{12}{5}$ are,

$\sin 胃 = - \frac{12}{13} \cos 胃 = - \frac{5}{13} c s c 胃 = - \frac{13}{12} s e c 胃 = - \frac{13}{5} c o t 胃 = \frac{5}{12}$

Step by step solution

Step 1 Given expression is,

$\tan 胃 = \frac{12}{5}, \sin 胃 < 0$

$胃$ lies in the third quadrant where $\sin 胃$ is negative and $\tan 胃$ is positive.

Let $伪$ be the reference angle for $胃$ then,role="math" localid="1646404662147" $\tan 胃 = \frac{b}{a} = \tan 伪$ .

So, $\tan 伪 = \frac{12}{5} = \frac{o p p . s i d e}{a d j . s i d e}$

Step 2 use the values b=12,a=5 to construct a triangle.

From the figure, we obtain $r = 13$ .

Step 3 Now write the remaining trigonometric values.

The remaining five trigonometric functions of the reference angle $伪$ are calculated as follows,

$\sin 伪 = \frac{b}{r} = \frac{12}{13} \cos 伪 = \frac{a}{r} = \frac{5}{13} c s c 伪 = \frac{r}{b} = \frac{13}{12} s e c 伪 = \frac{r}{a} = \frac{13}{5} c o t 伪 = \frac{a}{b} = \frac{5}{12}$

Step 4 Find the value of the remaining trigonometric functions of the angle θ.

$\sin 胃 = - \frac{b}{r} = - \frac{12}{13} \cos 胃 = - \frac{a}{r} = - \frac{5}{13} c s c 胃 = - \frac{r}{b} = - \frac{13}{12} s e c 胃 = - \frac{r}{a} = - \frac{13}{5} c o t 胃 = \frac{a}{b} = \frac{5}{12}$

These are the exact values of the remaining trigonometric functions.

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91影视

In Problems 16鈥�23, find the exact value of each of the remaining trigonometric functions.
$\tan 胃 = \frac{12}{5}, \sin 胃 < 0$ .

Short Answer

Step by step solution

Step 1 Given expression is,

Step 2 use the values b=12,a=5 to construct a triangle.

Step 3 Now write the remaining trigonometric values.

Step 4 Find the value of the remaining trigonometric functions of the angle θ.

One App. One Place for Learning.

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91影视

In Problems 16鈥�23, find the exact value of each of the remaining trigonometric functions.tan胃=125,sin胃<0.

Short Answer

Step by step solution

Step 1 Given expression is,

Step 2 use the values b=12,a=5 to construct a triangle.

Step 3 Now write the remaining trigonometric values.

Step 4 Find the value of the remaining trigonometric functions of the angle θ.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

In Problems 16鈥�23, find the exact value of each of the remaining trigonometric functions.
$\tan 胃 = \frac{12}{5}, \sin 胃 < 0$ .