Chapter 8: Q. 17 (page 516)

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

Short Answer

Expert verified

Required values of the trigonometric functions are:

$\sin θ = \frac{b}{c} = \frac{1}{\sqrt{5}} \cos θ = \frac{a}{c} = \frac{2}{\sqrt{5}} \tan θ = \frac{b}{a} = \frac{1}{2} c s c θ = \frac{c}{b} = \frac{\sqrt{5}}{1} = \sqrt{5} s e c θ = \frac{c}{a} = \frac{\sqrt{5}}{2} c o t θ = \frac{a}{b} = \frac{2}{1} = 2$

Step by step solution

Step 1. Given information

Let us consider the hypotenuse as 'c' , opposite as 'b' and the adjacent as 'a' .

Pythagorean Theorem:

$c^{2} = a^{2} + b^{2}$ , where a, b and c are adjacent, opposite and hypotenuse respectively.

Trigonometric Functions:

$\sin θ = \frac{b}{c} c s c θ = \frac{c}{b} \cos θ = \frac{a}{c} s e c θ = \frac{c}{a} \tan θ = \frac{b}{a} c o t θ = \frac{a}{b}$

Step 2. Calculation

$G i v e n, b = 1, c = \sqrt{5} B y P y t h a g o r e a n t h e o r e m, c^{2} = b^{2} + a^{2} a^{2} = c^{2} - b^{2} = {(\sqrt{5})}^{2} - 1^{2} = 5 - 1 = 4 a = \sqrt{4} = 2 n o w, \sin θ = \frac{b}{c} = \frac{1}{\sqrt{5}} \cos θ = \frac{a}{c} = \frac{2}{\sqrt{5}} \tan θ = \frac{b}{a} = \frac{1}{2} c s c θ = \frac{c}{b} = \frac{\sqrt{5}}{1} = \sqrt{5} s e c θ = \frac{c}{a} = \frac{\sqrt{5}}{2} c o t θ = \frac{a}{b} = \frac{2}{1} = 2$

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

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

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

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Discrete Mathematics

Pure Maths

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Geometry

Study anywhere. Anytime. Across all devices.

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