Chapter 6: Q. 17 (page 435)

In Problems 16–23, find the exact value of each of the remaining trigonometric functions.
$\tan θ = \frac{12}{5}, \sin θ < 0$ .

Short Answer

Expert verified

The exact value of the remaining trigonometric functions for the given expression $\tan θ = \frac{12}{5}$ are,

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

Step by step solution

Step 1 Given expression is,

$\tan θ = \frac{12}{5}, \sin θ < 0$

$θ$ lies in the third quadrant where $\sin θ$ is negative and $\tan θ$ is positive.

Let $α$ be the reference angle for $θ$ then,role="math" localid="1646404662147" $\tan θ = \frac{b}{a} = \tan α$ .

So, $\tan α = \frac{12}{5} = \frac{o p p . s i d e}{a d j . s i d e}$

Step 2 use the values b=12,a=5 to construct a triangle.

From the figure, we obtain $r = 13$ .

Step 3 Now write the remaining trigonometric values.

The remaining five trigonometric functions of the reference angle $α$ are calculated as follows,

$\sin α = \frac{b}{r} = \frac{12}{13} \cos α = \frac{a}{r} = \frac{5}{13} c s c α = \frac{r}{b} = \frac{13}{12} s e c α = \frac{r}{a} = \frac{13}{5} c o t α = \frac{a}{b} = \frac{5}{12}$

Step 4 Find the value of the remaining trigonometric functions of the angle θ.

$\sin θ = - \frac{b}{r} = - \frac{12}{13} \cos θ = - \frac{a}{r} = - \frac{5}{13} c s c θ = - \frac{r}{b} = - \frac{13}{12} s e c θ = - \frac{r}{a} = - \frac{13}{5} c o t θ = \frac{a}{b} = \frac{5}{12}$

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.
$\tan θ = \frac{12}{5}, \sin θ < 0$ .

Short Answer

Step by step solution

Step 1 Given expression is,

Step 2 use the values b=12,a=5 to construct a triangle.

Step 3 Now write the remaining trigonometric values.

Step 4 Find the value of the remaining trigonometric functions of the angle θ.

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In Problems 16–23, find the exact value of each of the remaining trigonometric functions.tanθ=125,sinθ<0.

Short Answer

Step by step solution

Step 1 Given expression is,

Step 2 use the values b=12,a=5 to construct a triangle.

Step 3 Now write the remaining trigonometric values.

Step 4 Find the value of the remaining trigonometric functions of the angle θ.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Calculus

Probability and Statistics

Theoretical and Mathematical Physics

Logic and Functions

Geometry

Study anywhere. Anytime. Across all devices.

In Problems 16–23, find the exact value of each of the remaining trigonometric functions.
$\tan θ = \frac{12}{5}, \sin θ < 0$ .