Chapter 8: Q. 13 (page 516)

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

Short Answer

Expert verified

The required trigonometric functions are:

$\sin θ = \frac{b}{c} = \frac{2 \sqrt{3}}{4} = \frac{\sqrt{3}}{2} c s c θ = \frac{c}{b} = \frac{4}{2 \sqrt{3}} = \frac{2}{\sqrt{3}} \cos θ = \frac{a}{c} = \frac{2}{4} = \frac{1}{2} s e c θ = \frac{c}{a} = \frac{4}{2} = 2 \tan θ = \frac{b}{a} = \frac{2 \sqrt{3}}{2} = \sqrt{3} c o t θ = \frac{a}{b} = \frac{2}{2 \sqrt{3}} = \frac{1}{\sqrt{3}}$

Step by step solution

Step 1. Given Information

From the figure, we have, $h y p o t e n u s e, c = 4$ and localid="1647160803805" $a d j a c e n t . a = 2$

Step 2. Formula Used

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 3. Calculation

We need to find the adjacent first,

So using Pythagorean Theorem,

$c^{2} = a^{2} + b^{2} b^{2} = c^{2} - a^{2}$

$b^{2} = 4^{2} - 2^{2} b^{2} = 16 - 4 b^{2} = 12$

$b = 2 \sqrt{3}$

Now, trigonometric functions are:

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

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Formula Used

Step 3. Calculation

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

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Formula Used

Step 3. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Pure Maths

Mechanics Maths

Applied Mathematics

Decision Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

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