Q. 77 A point on the terminal side of ... [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. 77 (page 381)

A point on the terminal side of an angle $胃$ in standard position is given. Find the exact value of each of the six trigonometric functions of $胃$ : $(- 3, 4)$

Short Answer

Expert verified

The exact values of the six trigonometric functions of $胃$ are,

$\sin 胃 = \frac{4}{5} \cos 胃 = \frac{- 3}{5} \tan 胃 = \frac{4}{- 3} \csc 胃 = \frac{5}{4} \sec 胃 = \frac{5}{- 3} \cot 胃 = \frac{- 3}{4}$

Step by step solution

Step 1. Given Information

The given point is $(- 3, 4)$ .

We need to find the exact value of each of the six trigonometric functions.

Step 2. Concept

Let $(x, y)$ be a point on the terminal side of the angle $胃$ in the standard position, which is also on the circle $x^{2} + y^{2} = r^{2}$ . Then,

localid="1646547465024" $\sin 胃 = \frac{y}{r} \cos 胃 = \frac{x}{r} \tan 胃 = \frac{y}{x} \csc 胃 = \frac{r}{y} \sec 胃 = \frac{r}{x} \cot 胃 = \frac{x}{y}$

Step 3. Finding the value of r

We are given the point $(- 3, 4)$ . Here $x = - 3, y = 4$ .

We know that,

$r = \sqrt{x^{2} + y^{2}} r = \sqrt{{(- 3)}^{2} + 4^{2}} r = \sqrt{9 + 16} r = \sqrt{25} r = 5$

Step 4. Finding the exact values of the six trigonometric functions

From the point $(- 3, 4)$ , we have $x = - 3, y = 4$ . Also, we have found that $r = 5$ . Therefore the trigonometric functions are,

$\sin 胃 = \frac{y}{r} = \frac{4}{5} \cos 胃 = \frac{x}{r} = \frac{- 3}{5} \tan 胃 = \frac{y}{x} = \frac{4}{- 3} \csc 胃 = \frac{r}{y} = \frac{5}{4} \sec 胃 = \frac{r}{x} = \frac{5}{- 3} \cot 胃 = \frac{x}{y} = \frac{- 3}{4}$

Step 5. Final Answer

The exact values of six trigonometric functions of $胃$ are,

$\sin 胃 = \frac{4}{5} \cos 胃 = \frac{- 3}{5} \tan 胃 = \frac{4}{- 3} \csc 胃 = \frac{5}{4} \sec 胃 = \frac{5}{- 3} \cot 胃 = \frac{- 3}{4}$

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91影视

A point on the terminal side of an angle $胃$ in standard position is given. Find the exact value of each of the six trigonometric functions of $胃$ : $(- 3, 4)$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Concept

Step 3. Finding the value of r

Step 4. Finding the exact values of the six trigonometric functions

Step 5. Final Answer

One App. One Place for Learning.

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91影视

A point on the terminal side of an angle 胃in standard position is given. Find the exact value of each of the six trigonometric functions of 胃:(-3,4)

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Concept

Step 3. Finding the value of r

Step 4. Finding the exact values of the six trigonometric functions

Step 5. Final Answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Logic and Functions

Decision Maths

Pure Maths

Probability and Statistics

Geometry

Study anywhere. Anytime. Across all devices.

A point on the terminal side of an angle $胃$ in standard position is given. Find the exact value of each of the six trigonometric functions of $胃$ : $(- 3, 4)$