Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 6: Q. 89 (page 381)

If $f (胃) = \sin 胃 = 0.1$ ,find $f (胃 + 蟺)$

Short Answer

Expert verified

The value of $f (胃 + 蟺) = - 0.1$

Step by step solution

Step 1. Given information

Given function $f (胃) = \sin 胃$

Step 2. Finding the value of f(θ+π)

For an angle $胃$ is standard position,let $P = (x, y)$ be the point on the terminal side of $胃$ that is also on the circle. $x^{2} + y^{2} = r^{2}$ .Then

localid="1647540879080" $\sin 胃 = \frac{y}{r} \cos 胃 = \frac{x}{r} \tan 胃 = \frac{y}{x} c s c 胃 = \frac{r}{y} s e c 胃 = \frac{r}{x} c o t 胃 = \frac{x}{y}$

Consider,

$f (胃) = \sin 胃 = 0.1$

That is

$\sin 胃 = \frac{y}{r} = 0.1$ so,that yis positive

Therefore, $胃$ is in 1st or 2nd quadrants.

Then $胃 + 蟺$ is in 3rd or 4th quadrant so that yis negative

Hence,

$f (胃 + 蟺) = - \frac{y}{r} = - \sin 胃 = - 0.1$

Therefore,the value of $f (胃 + 蟺) = - 0.1$

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91影视

If $f (胃) = \sin 胃 = 0.1$ ,find $f (胃 + 蟺)$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Finding the value of f(θ+π)

One App. One Place for Learning.

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91影视

Iff(胃)=sin胃=0.1,findf(胃+蟺)

Short Answer

Step by step solution

Step 1. Given information

Step 2. Finding the value of f(θ+π)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Theoretical and Mathematical Physics

Discrete Mathematics

Pure Maths

Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

If $f (胃) = \sin 胃 = 0.1$ ,find $f (胃 + 蟺)$