Chapter 6: Q.41 (page 395)

$\sin θ, \cos θ$ are given. Find the exact value of each of the four remaining trigonometric functions $\sin θ = - \frac{1}{3}, \cos θ = \frac{2 \sqrt{2}}{3}$

Short Answer

Expert verified

The value of $c s c θ = - 3, s e c θ = \frac{3}{2 \sqrt{2}}, \tan θ = - \frac{1}{2 \sqrt{2}}, c o t θ = - 2 \sqrt{2}$

Step by step solution

Step 1. Given information

Here $\sin θ = - \frac{1}{3}, \cos θ = \frac{2 \sqrt{2}}{3}$ are given.

We need to find the exact value of each of the four remaining trigonometric functions

. Finding the value of trigonometric functions cscθ and secθ

According to the question
$\sin θ = - \frac{1}{3} s o c s c θ = \frac{1}{\sin θ} = - \frac{1}{\frac{1}{3}} = - 3 \cos θ = \frac{2 \sqrt{2}}{3} t h e n s e c θ = \frac{1}{\cos θ} = \frac{1}{\frac{2 \sqrt{2}}{3}} = \frac{3}{2 \sqrt{2}}$

Step 3. Finding the value of the trigonometric function tanθ and cotθ

Since

$\tan θ = \frac{\sin θ}{\cos θ} = \frac{- \frac{1}{3}}{\frac{2 \sqrt{2}}{3}} \sin c e \sin θ = - \frac{1}{3} a n d \cos θ = \frac{2 \sqrt{2}}{3} = - \frac{1}{2 \sqrt{2}} a n d c o t θ = \frac{1}{\tan θ} = \frac{1}{- \frac{1}{2 \sqrt{2}}} = - 2 \sqrt{2}$

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$\sin θ, \cos θ$ are given. Find the exact value of each of the four remaining trigonometric functions $\sin θ = - \frac{1}{3}, \cos θ = \frac{2 \sqrt{2}}{3}$

Short Answer

Step by step solution

Step 1. Given information

. Finding the value of trigonometric functions cscθ and secθ

Step 3. Finding the value of the trigonometric function tanθ and cotθ

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sinθ,cosθ are given. Find the exact value of each of the four remaining trigonometric functionssinθ=-13,cosθ=223

Short Answer

Step by step solution

Step 1. Given information

. Finding the value of trigonometric functions cscθ and secθ

Step 3. Finding the value of the trigonometric function tanθ and cotθ

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Statistics

Probability and Statistics

Mechanics Maths

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Applied Mathematics

Study anywhere. Anytime. Across all devices.

$\sin θ, \cos θ$ are given. Find the exact value of each of the four remaining trigonometric functions $\sin θ = - \frac{1}{3}, \cos θ = \frac{2 \sqrt{2}}{3}$