Chapter 6: Q. 20 (page 437)

find the value of the remaining five trigonometric functions of $ϑ$
role="math" localid="1646316653225" $\cos ϑ = \frac{2}{3} \frac{3 π}{2} < ϑ < 2 π$

Short Answer

Expert verified

the value of the remaining five trigonometric functions of $ϑ$ are:

$\sin ϑ = - \frac{\sqrt{5}}{3} \tan ϑ = - \frac{\sqrt{5}}{2} \cos e c ϑ = \frac{- 3}{\sqrt{5}} s e c ϑ = \frac{3}{2} c o t ϑ = - \frac{2}{\sqrt{5}}$

Step by step solution

Step 1. Given information

$\cos ϑ = \frac{2}{3} \frac{3 π}{2} < ϑ < 2 π$

Step 2. Solving for sinϑ

We know ;

$\sin^{2} ϑ + \cos^{2} ϑ = 1$

Using this :

$\sin ϑ = \sqrt{1 - \cos^{2} ϑ} \sin ϑ = \sqrt{1 - {(\frac{2}{3})}^{2}} \sin ϑ = \sqrt{1 - \frac{4}{9}} \sin ϑ = \sqrt{\frac{5}{9}} \sin ϑ = \frac{\sqrt{5}}{3}$

Since theta is in fourth quadrant so,

$\sin ϑ = - \frac{\sqrt{5}}{3}$

Step 3. Solving for cosecϑ , secϑ , cotϑ

We know ;

$\cos e c ϑ = \frac{1}{\sin ϑ} s e c ϑ = \frac{1}{\cos ϑ} c o t ϑ = \frac{1}{\tan ϑ}$

Using the above identities :

$\cos e c ϑ = - \frac{3}{\sqrt{5}} s e c ϑ = \frac{3}{2} c o t ϑ = - \frac{2}{\sqrt{5}}$

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find the value of the remaining five trigonometric functions of $ϑ$
role="math" localid="1646316653225" $\cos ϑ = \frac{2}{3} \frac{3 π}{2} < ϑ < 2 π$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solving for sinϑ

Step 3. Solving for cosecϑ , secϑ , cotϑ

One App. One Place for Learning.

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find the value of the remaining five trigonometric functions of ϑrole="math" localid="1646316653225" cosϑ=233π2<ϑ<2π

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solving for sinϑ

Step 3. Solving for cosecϑ , secϑ , cotϑ

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Applied Mathematics

Pure Maths

Discrete Mathematics

Geometry

Logic and Functions

Study anywhere. Anytime. Across all devices.

find the value of the remaining five trigonometric functions of $ϑ$
role="math" localid="1646316653225" $\cos ϑ = \frac{2}{3} \frac{3 π}{2} < ϑ < 2 π$