Chapter 6: Q. 19 (page 435)

In Problems 16–23, find the exact value of each of the remaining trigonometric functions.
$\sin θ = \frac{12}{13}, θ$ lies in the quadrant ll.

Short Answer

Expert verified

The exact values of the remaining trigonometric functions of $\sin θ = \frac{12}{13}$ are,

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

Step by step solution

Step 1 Given expression is,

$\sin θ = \frac{12}{13}$ and $θ$ lies in the second quadrant.

So, $\sin θ, c s c θ$ are positive in the second quadrant and the remaining trigonometric functions are negative.

Let $α$ be the reference angle for $θ$ .

$\sin θ = \sin α$ .

So, $\sin θ = \frac{12}{13} = \frac{o p p o s i t e}{h y p o t e n u s e}$

Use $b = 12, r = 13$ to construct a triangle.

From the figure, we obtain $a = 5$ .

Step 2 Now calculate the remaining trigonometric functions.

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

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

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

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

These are the remaining trigonometric functions.

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In Problems 16–23, find the exact value of each of the remaining trigonometric functions.
$\sin θ = \frac{12}{13}, θ$ lies in the quadrant ll.

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 reference angle θ are given as,

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In Problems 16–23, find the exact value of each of the remaining trigonometric functions.sinθ=1213,θlies in the quadrant ll.

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 reference angle θ are given as,

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Pure Maths

Calculus

Statistics

Geometry

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In Problems 16–23, find the exact value of each of the remaining trigonometric functions.
$\sin θ = \frac{12}{13}, θ$ lies in the quadrant ll.