Chapter 6: Q.39 (page 395)

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

Short Answer

Expert verified

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

Step by step solution

Step 1. Given information

Here $\sin θ = \frac{1}{2}, \cos θ \frac{\sqrt{3}}{2}$ is 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

In this question

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

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

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

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.

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

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

Probability and Statistics

Pure Maths

Mechanics Maths

Statistics

Geometry

Decision Maths

Study anywhere. Anytime. Across all devices.

sinθ,cosθare given. Find the exact value of each of the four remaining trigonometric functions sinθ=12,cosθ32

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

Probability and Statistics

Pure Maths

Mechanics Maths

Statistics

Geometry

Decision Maths

Study anywhere. Anytime. Across all devices.

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