Chapter 6: Q.43 (page 395)

Find the exact value of each of the remaining trigonometric functions of $θ .$
localid="1646686875779" $\sin θ = \frac{12}{13}, θ i n s e c o n d q u a d r a n t .$

Short Answer

Expert verified

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

Step by step solution

Step 1. Given information

Here $\sin θ = \frac{12}{13}, θ i n s e c o n d q u a d r a n t .$ is given.

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

. Description of finding the value of cos θ

According to the question $\sin θ = \frac{12}{13} w h e r e θ l i e s o n 2 n d q u a d r a n t . W e k n o w t h a t \sin^{2} θ + \cos^{2} θ = 1 \cos θ = \pm \sqrt{1 - \sin^{2} θ} a n d \sin c e \sin θ i s o n 2 n d q u a d r a n t a l l o t h e r t r i g n o m e t r i c r a t i o s w i l l b e n e g a t i v e . h e n c e \cos θ = - \sqrt{1 - \sin^{2} θ} = - \sqrt{1 - \frac{12^{2}}{13^{2}}} = - \sqrt{1 - \frac{144}{169}} = - \sqrt{\frac{25}{169}} = - \frac{5}{13}$

Step 3. Describing about find the values of cscθ,secθ

Here

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

Step 4.Describing about find the values of tanθ and cotθ

We know that

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

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Find the exact value of each of the remaining trigonometric functions of $θ .$
localid="1646686875779" $\sin θ = \frac{12}{13}, θ i n s e c o n d q u a d r a n t .$

Short Answer

Step by step solution

Step 1. Given information

. Description of finding the value of cos θ

Step 3. Describing about find the values of cscθ,secθ

Step 4.Describing about find the values of tanθ and cotθ

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Find the exact value of each of the remaining trigonometric functions of θ.localid="1646686875779" sinθ=1213,θinsecondquadrant.

Short Answer

Step by step solution

Step 1. Given information

. Description of finding the value of cos θ

Step 3. Describing about find the values of cscθ,secθ

Step 4.Describing about find the values of tanθ and cotθ

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Statistics

Mechanics Maths

Decision Maths

Logic and Functions

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Find the exact value of each of the remaining trigonometric functions of $θ .$
localid="1646686875779" $\sin θ = \frac{12}{13}, θ i n s e c o n d q u a d r a n t .$