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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 7: Q. 2 (page 495)

$\sin^{2} \frac{胃}{2} = \frac{______}{2}$ .

Short Answer

Expert verified

$\sin^{2} \frac{胃}{2} = \frac{\underset{铃�}{1 - \cos (胃)}}{2}$ .

Step by step solution

Step 1. Given Data

The given incomplete equation is

$\sin^{2} \frac{胃}{2} = \frac{______}{2}$

Step 2. Explanation

as known $\sin^{2} 胃 = \frac{1 - \cos (2 胃)}{2}$

Substitute $\frac{胃}{2}$ for $胃$

localid="1646428514535" $\sin^{2} 胃 = \frac{1 - \cos (2 胃)}{2} \sin^{2} \frac{胃}{2} = \frac{1 - \cos (2 脳 \frac{胃}{2})}{2} \sin^{2} \frac{胃}{2} = \frac{1 - \cos (胃)}{2}$

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Most popular questions from this chapter

A rectangle is inscribed in a semicircle of radius $1$ . See the illustration.

Part (a): Express the area A of the rectangle as a function of the angle $胃$ shown in the illustration.

Part (b): Show that $A (胃) = \sin (2 胃)$ .

Part (c): Find the angle $胃$ that results in the largest area A.

Part (d): Find the dimensions of this largest rectangle.

Establish each identity.

${(a \sin 胃 + b \cos 胃)}^{2} + {(a \cos 胃 - b \sin 胃)}^{2} = a^{2} + b^{2}$

Rewrite over a common denominator:

$\frac{1}{1 - \cos (v)} + \frac{1}{1 + \cos (v)}$

Repeat Problem $107$ for $g (x) = \cos^{2} x$ .

If $x = 2 \tan 胃$ , express $\sin (2 胃)$ as a function ofx.

See all solutions

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sin2胃2=______2.

Short Answer

Step by step solution

Step 1. Given Data

Step 2. Explanation

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$\sin^{2} \frac{胃}{2} = \frac{______}{2}$ .