Chapter 6: Q.44 (page 395)

Find the exact value of each of the remaining trigonometric functions of $θ .$
$\cos θ = \frac{3}{5}, θ i s o n f o u r t h q u a d r a n t$

Short Answer

Expert verified

The value of $\sin θ = - \frac{4}{5}, s e c θ = \frac{5}{3}, c s c θ = - \frac{5}{4}, \tan θ = - \frac{4}{3} a n d c o t θ = - \frac{3}{4}$

Step by step solution

Step 1. Given information

Here $\cos θ = \frac{3}{5}, θ i s o n f o u r t h q u a d r a n t i s g i v e n .$

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

Step 2.Description of finding the value of sinθ

In this question $\cos θ = \frac{3}{5} W e k n o w t h a t \sin^{2} θ + \cos^{2} θ = 1 \sin θ = \pm \sqrt{1 - \cos^{2} θ} a n d \sin c e \cos θ i s o n f o u r t h q u a d r a n t a l l o t h e r t r i g n o m e t r i c r a t i o s w i l l b e n e g a t i v e . h e n c e \sin θ = - \sqrt{1 - \cos^{2} θ} = - \sqrt{1 - \frac{3^{2}}{5^{2}}} = - \sqrt{1 - \frac{9}{25}} = - \frac{4}{5}$

Step 3 . Finding the value of cscθ and secθ

According to the question

$\cos θ = \frac{3}{5} t h e n s e c θ = \frac{1}{\cos θ} = \frac{1}{\frac{3}{5}} = \frac{5}{3} c s c θ = \frac{1}{\sin θ} = \frac{1}{- \frac{4}{5}} = - \frac{5}{4}$

Step 4. Finding the value of tanθ and cot θ

Since $\sin θ = - \frac{4}{5} a n d \cos θ = \frac{3}{5} \tan θ = \frac{\sin θ}{\cos θ} = \frac{- \frac{4}{5}}{\frac{3}{5}} = \frac{- 4}{3} c o t θ = \frac{1}{\tan θ} = \frac{1}{- \frac{4}{3}} = - \frac{3}{4}$

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Find the exact value of each of the remaining trigonometric functions of $θ .$
$\cos θ = \frac{3}{5}, θ i s o n f o u r t h q u a d r a n t$

Short Answer

Step by step solution

Step 1. Given information

Step 2.Description of finding the value of sinθ

Step 3 . Finding the value of cscθ and secθ

Step 4. Finding the value of tanθ and cot θ

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Find the exact value of each of the remaining trigonometric functions of θ.cosθ=35,θisonfourthquadrant

Short Answer

Step by step solution

Step 1. Given information

Step 2.Description of finding the value of sinθ

Step 3 . Finding the value of cscθ and secθ

Step 4. Finding the value of tanθ and cot θ

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Find the exact value of each of the remaining trigonometric functions of $θ .$
$\cos θ = \frac{3}{5}, θ i s o n f o u r t h q u a d r a n t$