Q. 22 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. 22 (page 435)

In Problems 16鈥�23, find the exact value of each of the remaining trigonometric functions.
$s e c 胃 = 3$ , $\frac{3 蟺}{2} < 胃 < 2 蟺$

Short Answer

Expert verified

The exact values of the remaining trigonometric functions of $s e c 胃 = 3$ are,

role="math" localid="1646417178742" $\sin 胃 = - \frac{2 \sqrt{2}}{3} \cos 胃 = \frac{1}{3} \tan 胃 = - 2 \sqrt{2} c s c 胃 = - \frac{3 \sqrt{2}}{4} c o t 胃 = - \frac{1}{2 \sqrt{2}} = - \frac{\sqrt{2}}{4}$

Step by step solution

Step 1 Given expression is,

$s e c 胃 = 3$ and $\frac{3 蟺}{2} < 胃 < 2 蟺$ .

So, $胃$ lies in the fourth quadrant where $s e c 胃$ is positive.

Let $伪$ be the reference angle for $胃$ then $s e c 胃 = \frac{r}{a} = s e c 伪$ .

So, $s e c 伪 = \frac{3}{1} = \frac{O p p o s i t e}{A d j a c e n t}$

Use the values $r = 3, a = 1$ to construct a triangle.

From the figure, we obtain $b = 2 \sqrt{2}$ .

Step 2 Now calculate the remaining trigonometric functions.

The exact values of the remaining trigonometric functions of the reference angle $伪$ are,

localid="1646417520233" $\sin 伪 = \frac{b}{r} = \frac{2 \sqrt{2}}{3} \cos 伪 = \frac{a}{r} = \frac{1}{3} \tan 伪 = \frac{b}{a} = 2 \sqrt{2} c s c 伪 = \frac{r}{b} = \frac{3 \sqrt{2}}{4} c o t 伪 = \frac{a}{b} = \frac{1}{2 \sqrt{2}} = \frac{\sqrt{2}}{4}$

Step 3 The exact values of the remaining trigonometric functions of the angle θ are,

$\sin 胃 = - \frac{2 \sqrt{2}}{3} \cos 胃 = \frac{1}{3} \tan 胃 = - 2 \sqrt{2} c s c 胃 = - \frac{3 \sqrt{2}}{4} c o t 胃 = - \frac{1}{2 \sqrt{2}} = - \frac{\sqrt{2}}{4}$

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.
$s e c 胃 = 3$ , $\frac{3 蟺}{2} < 胃 < 2 蟺$

Short Answer

Step by step solution

Step 1 Given expression is,

Step 2 Now calculate the remaining trigonometric functions.

Step 3 The exact values of the remaining trigonometric functions of the angle θ are,

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91影视

In Problems 16鈥�23, find the exact value of each of the remaining trigonometric functions.sec胃=3,3蟺2<胃<2蟺

Short Answer

Step by step solution

Step 1 Given expression is,

Step 2 Now calculate the remaining trigonometric functions.

Step 3 The exact values of the remaining trigonometric functions of the angle θ are,

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Probability and Statistics

Logic and Functions

Statistics

Geometry

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In Problems 16鈥�23, find the exact value of each of the remaining trigonometric functions.
$s e c 胃 = 3$ , $\frac{3 蟺}{2} < 胃 < 2 蟺$