Q. 1 Find the exact value of the six ... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 8: Q. 1 (page 555)

Find the exact value of the six trigonometric functions of the angle $胃$ in the figure.

Short Answer

Expert verified

The ratio are,

$\sin 胃 = \frac{\sqrt{5}}{5} \cos 胃 = \frac{2 \sqrt{5}}{5} \tan 胃 = \frac{1}{2} co t 胃 = 2 c s c 胃 = \sqrt{5} s e c 胃 = \frac{\sqrt{5}}{2}$

Step by step solution

Step 1. Given Information

The given triangle is,

Step 2. Determine the hypotenuse

In the given triangle, $p = 3, b = 6$ .
Use Pythagoras theorem, to determine the hypotenuse.

role="math" localid="1646825617277" $\begin{array}{rcl} h^{2} & = & p^{2} + b^{2} \\ h^{2} & = & 3^{2} + 6^{2} \\ h^{2} & = & 9 + 36 \\ h & = & \sqrt{45} \\ = & 3 \sqrt{5} \end{array}$

Step 3. Determine the trigonometric ratios.

Determine the trigonometric ratios.

$\sin 胃 = \frac{p}{h} = \frac{3}{3 \sqrt{5}} = \frac{1}{\sqrt{5}} = \frac{\sqrt{5}}{5} \cos 胃 = \frac{b}{h} = \frac{6}{3 \sqrt{5}} = \frac{2}{\sqrt{5}} = \frac{2 \sqrt{5}}{5} \tan 胃 = \frac{p}{b} = \frac{3}{6} = \frac{1}{2} co t 胃 = \frac{b}{p} = \frac{6}{3} = 2 c s c 胃 = \frac{h}{p} = \frac{3 \sqrt{5}}{3} = \sqrt{5} s e c 胃 = \frac{h}{b} = \frac{3 \sqrt{5}}{6} = \frac{\sqrt{5}}{2}$

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91影视

Find the exact value of the six trigonometric functions of the angle $胃$ in the figure.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Determine the hypotenuse

Step 3. Determine the trigonometric ratios.

One App. One Place for Learning.

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91影视

Find the exact value of the six trigonometric functions of the angle 胃in the figure.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Determine the hypotenuse

Step 3. Determine the trigonometric ratios.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Decision Maths

Logic and Functions

Probability and Statistics

Calculus

Statistics

Study anywhere. Anytime. Across all devices.

Find the exact value of the six trigonometric functions of the angle $胃$ in the figure.