Chapter 8: Q.1 (page 507)

Find the exact value of six trigonometrical functions of the angle $θ$

Short Answer

Expert verified

The simplified value is $si n θ = \frac{p e r p e n d i c u l a r}{h y p e \tan o u s} = \frac{4}{5} \cos θ = \frac{b a s e}{h y p e \tan o u s} = \frac{3}{5} \tan θ = \frac{p e r p e n d i c u l a r}{b a s e} = \frac{4}{3} c o t θ = \frac{1}{\tan θ} = \frac{3}{4} c s c θ = \frac{1}{\sin θ} = \frac{5}{4} s e c θ = \frac{1}{\cos θ} = \frac{5}{3}$

Step by step solution

Step 1. Given information

The given data from the graph is $p e r p e n d i c u l a r = 4 b a s e = 3$

Step 2. Write all the trigonometrical function

Here, $p e r p e n d i c u l a r = 4 b a s e = 3$

By Pythagoras theorem, $h^{2} = p^{2} + b^{2} = 3^{2} + 4^{2} = 9 + 16 = 25 h = 5$

role="math" localid="1646655843647" $si n θ = \frac{p e r p e n d i c u l a r}{h y p e \tan o u s} = \frac{4}{5} \cos θ = \frac{b a s e}{h y p e \tan o u s} = \frac{3}{5} \tan θ = \frac{p e r p e n d i c u l a r}{b a s e} = \frac{4}{3} c o t θ = \frac{1}{\tan θ} = \frac{3}{4} c s c θ = \frac{1}{\sin θ} = \frac{5}{4} s e c θ = \frac{1}{\cos θ} = \frac{5}{3}$

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Find the exact value of six trigonometrical functions of the angle $θ$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Write all the trigonometrical function

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Find the exact value of six trigonometrical functions of the angleθ

Short Answer

Step by step solution

Step 1. Given information

Step 2. Write all the trigonometrical function

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Discrete Mathematics

Theoretical and Mathematical Physics

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Logic and Functions

Study anywhere. Anytime. Across all devices.

Find the exact value of six trigonometrical functions of the angle $θ$