Chapter 6: Q.47 (page 395)

Find the exact value of each of the remaining trigonometric functions of $θ$ .
$\sin θ = \frac{5}{13}, 90^{o} < θ < 180^{o}$

Short Answer

Expert verified

The exact values are $\cos θ = - \frac{12}{13}, s e c θ = - \frac{13}{12}, c s c θ = \frac{13}{5}, \tan θ = - \frac{5}{12}, c o t θ = - \frac{12}{5}$

Step by step solution

Step 1. Given information

Here $\sin θ = \frac{5}{13}, 90^{o} < θ < 180^{o}$ are given.

We have to find the exact value of each of the remaining trigonometric functions.

Step 2.Description of finding the value cosθ.

In this question $\sin θ = \frac{5}{13} W e k n o w t h a t \sin^{2} θ + \cos^{2} θ = 1 \cos θ = \pm \sqrt{1 - \sin^{2} θ}, h e r e θ l i e s o n 90^{o} < θ < 180^{o} s o \sin θ i s o n s e c o n d q u a d r a n t a l l o t h e r e x c e p t \sin θ a n d c s c θ a r e w i l l b e n e g a t i v e . h e n c e \cos θ = - \sqrt{1 - \sin^{2} θ} = - \sqrt{1 - \frac{5^{2}}{13^{2}}} = - \sqrt{1 - \frac{25}{169}} = - \frac{12}{13}$

Step 3. finding the value of secθ and cscθ

Here

$\cos θ = - \frac{12}{13}, t h e n s e c θ = \frac{1}{\cos θ} = \frac{1}{- \frac{12}{13}} = - \frac{13}{12} c s c θ = \frac{1}{\sin θ} = \frac{1}{\frac{5}{13}} = \frac{13}{5}$

Step 4. Finding the value for tanθ and cotθ

We know that

\tan θ = \frac{\sin θ}{\cos θ}, \sin θ = \frac{5}{13} a n d \cos θ = - \frac{12}{13} = \frac{\frac{5}{13}}{\frac{- 12}{13}} = - \frac{5}{12} c o t θ = \frac{1}{\tan θ} = \frac{1}{- \frac{5}{12}} = - \frac{12}{5}

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 each of the remaining trigonometric functions of $θ$ .
$\sin θ = \frac{5}{13}, 90^{o} < θ < 180^{o}$

Short Answer

Step by step solution

Step 1. Given information

Step 2.Description of finding the value cosθ.

Step 3. finding the value of secθ and cscθ

Step 4. Finding the value for tanθ and cotθ

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Mechanics Maths

Applied Mathematics

Theoretical and Mathematical Physics

Pure Maths

Statistics

Study anywhere. Anytime. Across all devices.

Find the exact value of each of the remaining trigonometric functions of θ.sinθ=513,90o<θ<180o

Short Answer

Step by step solution

Step 1. Given information

Step 2.Description of finding the value cosθ.

Step 3. finding the value of secθ and cscθ

Step 4. Finding the value for tanθ and cotθ

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Mechanics Maths

Applied Mathematics

Theoretical and Mathematical Physics

Pure Maths

Statistics

Study anywhere. Anytime. Across all devices.

Find the exact value of each of the remaining trigonometric functions of $θ$ .
$\sin θ = \frac{5}{13}, 90^{o} < θ < 180^{o}$