Chapter 8: Q.2 (page 553)

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

Short Answer

Expert verified

The simplifed value is $si n θ = \frac{p e r p e n d i c u l a r}{h y p e \tan o u s} = \frac{2 \sqrt{3}}{4} = \frac{\sqrt{3}}{2} \cos θ = \frac{b a s e}{h y p e \tan o u s} = \frac{2}{4} = \frac{1}{2} \tan θ = \frac{p e r p e n d i c u l a r}{b a s e} = \frac{2 \sqrt{3}}{2} = \sqrt{3} c o t θ = \frac{1}{\tan θ} = \frac{1}{\sqrt{3}} c s c θ = \frac{1}{\sin θ} = \frac{2}{\sqrt{3}} s e c θ = \frac{1}{\cos θ} = 2$

Step by step solution

Step 1. Given information

The given data from the graph is $H y p o t e n u s e = 4 b a s e = 2$

Step 2. Write all the trigonometrical function

Here $H y p o t e n u s e = 4 b a s e = 2$

, $h^{2} = p^{2} + b^{2} 4^{2} = p^{2} + 2^{2} 4^{2} - 2^{2} = p^{2} 16 - 4 = p^{2} p^{2} = 12 p = 2 \sqrt{3}$

role="math" localid="1646735032038"

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{2 \sqrt{3}}{4} = \frac{\sqrt{3}}{2} \cos θ = \frac{b a s e}{h y p e \tan o u s} = \frac{2}{4} = \frac{1}{2} \tan θ = \frac{p e r p e n d i c u l a r}{b a s e} = \frac{2 \sqrt{3}}{2} = \sqrt{3} c o t θ = \frac{1}{\tan θ} = \frac{1}{\sqrt{3}} c s c θ = \frac{1}{\sin θ} = \frac{2}{\sqrt{3}} s e c θ = \frac{1}{\cos θ} = 2

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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 angle θ

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

Statistics

Probability and Statistics

Logic and Functions

Decision Maths

Mechanics Maths

Pure Maths

Study anywhere. Anytime. Across all devices.

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