Chapter 6: Q. 22 (page 435)

In Problems 16–23, find the exact value of each of the remaining trigonometric functions.
$s e c θ = 3$ , $\frac{3 π}{2} < θ < 2 π$

Short Answer

Expert verified

The exact values of the remaining trigonometric functions of $s e c θ = 3$ are,

role="math" localid="1646417178742" $\sin θ = - \frac{2 \sqrt{2}}{3} \cos θ = \frac{1}{3} \tan θ = - 2 \sqrt{2} c s c θ = - \frac{3 \sqrt{2}}{4} c o t θ = - \frac{1}{2 \sqrt{2}} = - \frac{\sqrt{2}}{4}$

Step by step solution

Step 1 Given expression is,

$s e c θ = 3$ and $\frac{3 π}{2} < θ < 2 π$ .

So, $θ$ lies in the fourth quadrant where $s e c θ$ is positive.

Let $α$ be the reference angle for $θ$ then $s e c θ = \frac{r}{a} = s e c α$ .

So, $s e c α = \frac{3}{1} = \frac{O p p o s i t e}{A d j a c e n t}$

Use the values $r = 3, a = 1$ to construct a triangle.

From the figure, we obtain $b = 2 \sqrt{2}$ .

Step 2 Now calculate the remaining trigonometric functions.

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

localid="1646417520233" $\sin α = \frac{b}{r} = \frac{2 \sqrt{2}}{3} \cos α = \frac{a}{r} = \frac{1}{3} \tan α = \frac{b}{a} = 2 \sqrt{2} c s c α = \frac{r}{b} = \frac{3 \sqrt{2}}{4} c o t α = \frac{a}{b} = \frac{1}{2 \sqrt{2}} = \frac{\sqrt{2}}{4}$

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

$\sin θ = - \frac{2 \sqrt{2}}{3} \cos θ = \frac{1}{3} \tan θ = - 2 \sqrt{2} c s c θ = - \frac{3 \sqrt{2}}{4} c o t θ = - \frac{1}{2 \sqrt{2}} = - \frac{\sqrt{2}}{4}$

These are the exact values of the remaining trigonometric functions.

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In Problems 16–23, find the exact value of each of the remaining trigonometric functions.
$s e c θ = 3$ , $\frac{3 π}{2} < θ < 2 π$

Short Answer

Step by step solution

Step 1 Given expression is,

Step 2 Now calculate the remaining trigonometric functions.

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

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In Problems 16–23, find the exact value of each of the remaining trigonometric functions.secθ=3,3π2<θ<2π

Short Answer

Step by step solution

Step 1 Given expression is,

Step 2 Now calculate 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

Logic and Functions

Decision Maths

Probability and Statistics

Discrete Mathematics

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Study anywhere. Anytime. Across all devices.

In Problems 16–23, find the exact value of each of the remaining trigonometric functions.
$s e c θ = 3$ , $\frac{3 π}{2} < θ < 2 π$