Chapter 8: Q. 11 (page 516)

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

Short Answer

Expert verified

The required six trigonometric functions are:

$\sin ϑ = \frac{3}{\sqrt{13}} \cos θ = \frac{2}{\sqrt{13}} \tan θ = \frac{3}{2} c s c θ = \frac{\sqrt{13}}{3} s e c θ = \frac{\sqrt{13}}{2} c o t θ = \frac{2}{3}$

Step by step solution

Step 1. Given Information

From the figure, we have

$a d j a c e n t, a = 2$ and $o p p o s i t e, b = 3$

Step 2. Formula Used

Pythagorean Theorem: $a^{2} + b^{2} = c^{2}$

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 have, $a d j a c e n t, a = 2$ and $o p p o s i t e, b = 3$

We have to find hypotenuse, c

Using Pythagorean Theorem,

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

$c^{2} = 2^{2} + 3^{2}$

$c^{2} = 4 + 9$

$c^{2} = 13$

$c = \sqrt{13}$

Now, the value of the trigonometric functions are:

$\sin θ = \frac{b}{c} = \frac{3}{\sqrt{13}}$ $\cos θ = \frac{a}{c} = \frac{2}{\sqrt{13}}$

$\tan θ = \frac{b}{a} = \frac{3}{2}$ $c s c θ = \frac{c}{b} = \frac{\sqrt{13}}{3}$

$s e c θ \frac{c}{a} = \frac{\sqrt{13}}{2}$ $c o t θ \frac{a}{b} = \frac{2}{3}$

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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. Formula Used

Step 3. Calculation

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Find the exact value of the 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

Geometry

Statistics

Applied Mathematics

Pure Maths

Calculus

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

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