Chapter 6: Q.46 (page 395)

Find the exact value of each of the remaining trigonometric functions of $θ$
$\sin θ = - \frac{5}{13}, w h e r e θ l i e s o n 3 r d q u a d r a n t .$

Short Answer

Expert verified

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

Step by step solution

Step 1. Given information

Here $\sin θ = - \frac{5}{13} w h e r e θ l i e s o n 3 r d q u a d r a n t$

we have to find exact value of each of the remaining trigonometric functions

. description of finding the value of cosθ

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

Step 3. Finding the values of cscθ and secθ

in this question

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

Step 4. Finding the values of tan θ, cotθ

Since

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

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Find the exact value of each of the remaining trigonometric functions of $θ$
$\sin θ = - \frac{5}{13}, w h e r e θ l i e s o n 3 r d q u a d r a n t .$

Short Answer

Step by step solution

Step 1. Given information

. description of finding the value of cosθ

Step 3. Finding the values of cscθ and secθ

Step 4. Finding the values of tan θ, cotθ

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Find the exact value of each of the remaining trigonometric functions of θsinθ=-513,whereθlieson3rdquadrant.

Short Answer

Step by step solution

Step 1. Given information

. description of finding the value of cosθ

Step 3. Finding the values of cscθ and secθ

Step 4. Finding the values of tan θ, cotθ

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Theoretical and Mathematical Physics

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Calculus

Study anywhere. Anytime. Across all devices.

Find the exact value of each of the remaining trigonometric functions of $θ$
$\sin θ = - \frac{5}{13}, w h e r e θ l i e s o n 3 r d q u a d r a n t .$