Chapter 6: Q. 20 (page 435)

In Problems 16–23, find the exact value of each of the remaining trigonometric functions.
$\sin θ = - \frac{5}{13}, \frac{3 π}{2} < θ < 2 π$

Short Answer

Expert verified

The exact values of the remaining trigonometric functions of $\sin θ = - \frac{5}{13}$ are,

$\sin θ = - \frac{5}{13} \cos θ = \frac{12}{13} \tan θ = - \frac{5}{12} c s c θ = - \frac{13}{5} s e c θ = \frac{13}{12} co t θ = - \frac{12}{5}$

Step by step solution

Step 1 Given expression is,

$\sin θ = - \frac{5}{13}$ and $\frac{3 π}{2} < θ < 2 π$ .

So, $θ$ lies in the fourth quadrant, where $\cos θ, s e c θ$ are positive and the remaining trigonometric functions are negative.

Let $α$ be the reference angle for $θ$ then, $\sin θ = \frac{b}{r} = \sin α$ .

So, $\sin α = \frac{5}{13} = \frac{O p p o s i t e}{H y p o t e n u s e}$ .

Use the values $b = 5, r = 13$ to construct a triangle.

From the figure, we obtain $a = 12$ .

Step 2 Now calculate the remaining trigonometric functions.

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

role="math" localid="1646414505856" $\cos α = \frac{a}{r} = \frac{12}{13} \tan α = \frac{b}{a} = \frac{5}{12} c s c α = \frac{r}{b} = \frac{13}{5} s e c α = \frac{r}{a} = \frac{13}{12} co t α = \frac{a}{b} = \frac{12}{5}$

Step 3 Now find the exact values for the remaining trigonometric function of the reference angle θ.

$\sin θ = - \frac{5}{13} \cos θ = \frac{12}{13} \tan θ = - \frac{5}{12} c s c θ = - \frac{13}{5} s e c θ = \frac{13}{12} co t θ = - \frac{12}{5}$

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In Problems 16–23, find the exact value of each of the remaining trigonometric functions.
$\sin θ = - \frac{5}{13}, \frac{3 π}{2} < θ < 2 π$

Short Answer

Step by step solution

Step 1 Given expression is,

Step 2 Now calculate the remaining trigonometric functions.

Step 3 Now find the exact values for the remaining trigonometric function of the reference angle θ.

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In Problems 16–23, find the exact value of each of the remaining trigonometric functions.sinθ=-513,3π2<θ<2π

Short Answer

Step by step solution

Step 1 Given expression is,

Step 2 Now calculate the remaining trigonometric functions.

Step 3 Now find the exact values for the remaining trigonometric function of the reference angle θ.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Geometry

Decision Maths

Mechanics Maths

Logic and Functions

Statistics

Study anywhere. Anytime. Across all devices.

In Problems 16–23, find the exact value of each of the remaining trigonometric functions.
$\sin θ = - \frac{5}{13}, \frac{3 π}{2} < θ < 2 π$