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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 6: Q 100. (page 381)

If $f (胃) = \sin 胃$ and $g (胃) = \cos 胃$ . Find the exact value of the function given below if $胃 = 60 掳$ . Do not use a calculator.
Function is ${[g (胃)]}^{2}$ .

Short Answer

Expert verified

The value of the function ${[g (胃)]}^{2}$ is $\frac{1}{4}$ .

Step by step solution

01

Step 1. Given information.

Consider the given function ${[g (胃)]}^{2}$ where localid="1646396871570" $g (胃) = \cos 胃$ and the value of $胃 = 60 掳$ .

02

Step 2. Finding gθ2.

In the trigonometric standard angle the value of $\cos 60 掳 = \frac{1}{2}$ .

Substitute the value in function ${[g (胃)]}^{2}$ .

${[g (胃)]}^{2} = {[\cos 60 掳]}^{2} = {[\frac{1}{2}]}^{2} = \frac{1}{4}$

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Most popular questions from this chapter

In the problem, $s$ denotes the length of the arc of a circle of radius $r$ subtended by the central angle $胃$ . Find the missing quantity. Round answers to three decimal places.

$r = 6$ feet, $胃 = 2$ radians, $s = ?$

Find the exact values of the six trigonometric functions of the given angle. If any are not defined, say "not defined." Do not use a calculator.

$\frac{13 蟺}{6}$

Convert each angle in degrees to radians. Express your answer as a multiple of $蟺$ .

$- 30 掳$

Pulleys Two pulleys, one with radius $r_{1}$ and the other with radius $r_{2}$ , are connected by a belt. The pulley with radius $r_{1}$ rotates at $v_{1}$ revolutions per minute, whereas the pulley with

radius $r_{2}$ rotates at $v_{2}$ revolutions per minute. Show thatrole="math" localid="1646296862603" $\frac{r_{1}}{r_{2}} = \frac{蝇_{1}}{蝇_{2}}$

Find the exact value of each expression. Do not use a calculator.

$\sec 蟺 - \csc \frac{蟺}{2}$

See all solutions

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