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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 32. (page 381)

Find the exact value of each expression. Do not use a calculator.
$\sin 30 掳 - \cos 45 掳$

Short Answer

Expert verified

The exact value of $\sin 30 掳 - \cos 45 掳 = \frac{1 - \sqrt{2}}{2}$

Step by step solution

01

Step 1. Given information

$\sin 30 掳 - \cos 45 掳$

02

Step 2. Solution

$\sin 45 掳 = \frac{1}{2} \cos 45 掳 = \frac{1}{\sqrt{2}} Putting the values in the given expression we get, \frac{1}{2} - \frac{1}{\sqrt{2}} = \frac{\sqrt{2} - 2}{2 \sqrt{2}} = \frac{\sqrt{2} (1 - \sqrt{2})}{2 \sqrt{2}} = \frac{1 - \sqrt{2}}{2} So, \sin 30 掳 - \cos 45 掳 = \frac{1 - \sqrt{2}}{2}$

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