Q. 17 Find the exact value of the six ... [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 8: Q. 17 (page 516)

Find the exact value of the six trigonometric functions of the angle $胃$ in each figure.

Short Answer

Expert verified

Required values of the trigonometric functions are:

$\sin 胃 = \frac{b}{c} = \frac{1}{\sqrt{5}} \cos 胃 = \frac{a}{c} = \frac{2}{\sqrt{5}} \tan 胃 = \frac{b}{a} = \frac{1}{2} c s c 胃 = \frac{c}{b} = \frac{\sqrt{5}}{1} = \sqrt{5} s e c 胃 = \frac{c}{a} = \frac{\sqrt{5}}{2} c o t 胃 = \frac{a}{b} = \frac{2}{1} = 2$

Step by step solution

Step 1. Given information

Let us consider the hypotenuse as 'c' , opposite as 'b' and the adjacent as 'a' .

Pythagorean Theorem:

$c^{2} = a^{2} + b^{2}$ , where a, b and c are adjacent, opposite and hypotenuse respectively.

Trigonometric Functions:

$\sin 胃 = \frac{b}{c} c s c 胃 = \frac{c}{b} \cos 胃 = \frac{a}{c} s e c 胃 = \frac{c}{a} \tan 胃 = \frac{b}{a} c o t 胃 = \frac{a}{b}$

Step 2. Calculation

$G i v e n, b = 1, c = \sqrt{5} B y P y t h a g o r e a n t h e o r e m, c^{2} = b^{2} + a^{2} a^{2} = c^{2} - b^{2} = {(\sqrt{5})}^{2} - 1^{2} = 5 - 1 = 4 a = \sqrt{4} = 2 n o w, \sin 胃 = \frac{b}{c} = \frac{1}{\sqrt{5}} \cos 胃 = \frac{a}{c} = \frac{2}{\sqrt{5}} \tan 胃 = \frac{b}{a} = \frac{1}{2} c s c 胃 = \frac{c}{b} = \frac{\sqrt{5}}{1} = \sqrt{5} s e c 胃 = \frac{c}{a} = \frac{\sqrt{5}}{2} c o t 胃 = \frac{a}{b} = \frac{2}{1} = 2$

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91影视

Find the exact value of the six trigonometric functions of the angle $胃$ in each figure.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

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91影视

Find the exact value of the six trigonometric functions of the angle 胃 in each figure.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Discrete Mathematics

Logic and Functions

Statistics

Geometry

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Find the exact value of the six trigonometric functions of the angle $胃$ in each figure.