Chapter 6: Q. 23 (page 435)

In Problems 16–23, find the exact value of each of the remaining trigonometric functions.
$c o t θ = - 2, \frac{π}{2} < θ < π$ .

Short Answer

Expert verified

The exact values of the remaining trigonometric functions of $c o t θ = - 2$ are,

$\sin θ = \frac{\sqrt{5}}{5} \cos θ = - \frac{2 \sqrt{5}}{5} \tan θ = - \frac{1}{2} c s c θ = \sqrt{5} s e c θ = - \frac{\sqrt{5}}{2}$

Step by step solution

Step 1 Given expression is,

$c o t θ = - 2$ and $\frac{π}{2} < θ < 2 π$ .

So, $θ$ lies in the second quadrant where $c o t θ$ is negative.

Let $α$ be the reference angle for $θ$ then $c o t θ = \frac{a}{b} = c o t α$ .

So, $c o t α = \frac{2}{1} = \frac{A d j a c e n t}{O p p o s i t e}$

Use the values $a = 2, b = 1$ to construct a triangle.

From the figure, we can obtain $r = \sqrt{5}$ .

Step 2 Now find the exact values of the remaining trigonometric functions.

The exact values of the remaining trigonometric functions of the reference angle $α$ are,

role="math" localid="1646419068024" $\sin α = \frac{b}{r} = \frac{1}{\sqrt{5}} = \frac{\sqrt{5}}{5} \cos α = \frac{a}{r} = \frac{2}{\sqrt{5}} = \frac{2 \sqrt{5}}{5} \tan α = \frac{b}{a} = \frac{1}{2} c s c α = \frac{r}{b} = \frac{\sqrt{5}}{1} = \sqrt{5} s e c α = \frac{r}{a} = \frac{\sqrt{5}}{2}$

Step 3 The exact values of the remaining trigonometric functions of the angle θ are,

$\sin θ = \frac{\sqrt{5}}{5} \cos θ = - \frac{2 \sqrt{5}}{5} \tan θ = - \frac{1}{2} c s c θ = \sqrt{5} s e c θ = - \frac{\sqrt{5}}{2}$

These are the exact values of the remaining trigonometric functions.

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.

In Problems 16–23, find the exact value of each of the remaining trigonometric functions.
$c o t θ = - 2, \frac{π}{2} < θ < π$ .

Short Answer

Step by step solution

Step 1 Given expression is,

Step 2 Now find the exact values of the remaining trigonometric functions.

Step 3 The exact values of the remaining trigonometric functions of the angle θ are,

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Statistics

Pure Maths

Probability and Statistics

Calculus

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In Problems 16–23, find the exact value of each of the remaining trigonometric functions.cotθ=-2,π2<θ<π.

Short Answer

Step by step solution

Step 1 Given expression is,

Step 2 Now find the exact values of the remaining trigonometric functions.

Step 3 The exact values of the remaining trigonometric functions of the angle θ are,

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Statistics

Pure Maths

Probability and Statistics

Calculus

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In Problems 16–23, find the exact value of each of the remaining trigonometric functions.
$c o t θ = - 2, \frac{π}{2} < θ < π$ .