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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. 12 (page 436)

find the exact value of the expression
$2 \sin^{2} 60 掳 - 3 \cos 45 掳$

Short Answer

Expert verified

$2 \sin^{2} 60 掳 - 3 \cos 45 掳 = 3 (\frac{1}{2} - \frac{1}{\sqrt{2}})$

Step by step solution

Step 1. Rewriting the expression

Given expression can be written as $2 {(\sin 60 掳)}^{2} - \cos 45 掳$

Step 2. Calculations

$\sin 60 掳 = \frac{\sqrt{3}}{2} \cos 45 掳 = \frac{1}{\sqrt{2}} S o 2 {(\sin 60 掳)}^{2} - 3 \cos 45 掳 = 2 {(\frac{\sqrt{3}}{2})}^{2} - \frac{3}{\sqrt{2}} = \frac{3}{2} - \frac{3}{\sqrt{2}} = 3 (\frac{1}{2} - \frac{1}{\sqrt{2}})$

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Most popular questions from this chapter

In Problems $1 - 3$ , convert each angle in degrees to radians. Express your answer as a multiple of $蟺$ .

$1 . 260 掳$

Convert angle in radian to degree-

$\frac{蟺}{3}$

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

$- 90 掳$

In problems 13-20, $P (x, y)$ is the point on the unit circle that corresponds to a real number $t$ . Find the exact values of the six trigonometric functions of $t$ .

$(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2})$ .

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.

$210 掳$

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find the exact value of the expression 2sin260掳-3cos45掳

Short Answer

Step by step solution

Step 1. Rewriting the expression

Step 2. Calculations

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Most popular questions from this chapter

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find the exact value of the expression
$2 \sin^{2} 60 掳 - 3 \cos 45 掳$