Chapter 8: Q. 15 (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 six trigonometric functions are:

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

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

$G i v e n, b = \sqrt{2}, a = 1 B y P y t h a g o r e a n t h e o r e m, c^{2} = b^{2} + a^{2} = {(\sqrt{2})}^{2} + 1^{2} = 2 + 1 = 3 c = \sqrt{3} n o w, \sin θ = \frac{b}{c} = \frac{\sqrt{2}}{\sqrt{3}} \cos θ = \frac{a}{c} = \frac{1}{\sqrt{3}} \tan θ = \frac{b}{a} = \frac{\sqrt{2}}{1} = \sqrt{2} c s c θ = \frac{c}{b} = \frac{\sqrt{3}}{\sqrt{2}} s e c θ = \frac{c}{a} = \frac{\sqrt{3}}{1} = \sqrt{3} c o t θ = \frac{a}{b} = \frac{1}{\sqrt{2}}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

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

Pure Maths

Mechanics Maths

Calculus

Statistics

Applied Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

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. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Mechanics Maths

Calculus

Statistics

Applied Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

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