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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 8: Q.2 (page 553)

Find the exact value of six trigonometrical functions of the angle $胃$

Short Answer

Expert verified

The simplifed value is $si n 胃 = \frac{p e r p e n d i c u l a r}{h y p e \tan o u s} = \frac{2 \sqrt{3}}{4} = \frac{\sqrt{3}}{2} \cos 胃 = \frac{b a s e}{h y p e \tan o u s} = \frac{2}{4} = \frac{1}{2} \tan 胃 = \frac{p e r p e n d i c u l a r}{b a s e} = \frac{2 \sqrt{3}}{2} = \sqrt{3} c o t 胃 = \frac{1}{\tan 胃} = \frac{1}{\sqrt{3}} c s c 胃 = \frac{1}{\sin 胃} = \frac{2}{\sqrt{3}} s e c 胃 = \frac{1}{\cos 胃} = 2$

Step by step solution

01

Step 1. Given information

The given data from the graph is $H y p o t e n u s e = 4 b a s e = 2$

02

Step 2. Write all the trigonometrical function

Here $H y p o t e n u s e = 4 b a s e = 2$

, $h^{2} = p^{2} + b^{2} 4^{2} = p^{2} + 2^{2} 4^{2} - 2^{2} = p^{2} 16 - 4 = p^{2} p^{2} = 12 p = 2 \sqrt{3}$

role="math" localid="1646735032038"

si n 胃 = \frac{p e r p e n d i c u l a r}{h y p e \tan o u s} = \frac{2 \sqrt{3}}{4} = \frac{\sqrt{3}}{2} \cos 胃 = \frac{b a s e}{h y p e \tan o u s} = \frac{2}{4} = \frac{1}{2} \tan 胃 = \frac{p e r p e n d i c u l a r}{b a s e} = \frac{2 \sqrt{3}}{2} = \sqrt{3} c o t 胃 = \frac{1}{\tan 胃} = \frac{1}{\sqrt{3}} c s c 胃 = \frac{1}{\sin 胃} = \frac{2}{\sqrt{3}} s e c 胃 = \frac{1}{\cos 胃} = 2

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