Chapter 6: Q. 16 (page 435)

In Problems 16–23, find the exact value of each of the remaining trigonometric functions.
$\sin θ = \frac{4}{5}, θ$ is acute.

Short Answer

Expert verified

The exact value of $\sin θ = \frac{4}{5}$ of the remaining trigonometric functions are,

role="math" localid="1646366252886" $1 . c s c θ = \frac{5}{4} 2 . \cos θ = \frac{3}{5} 3 . s e c θ = \frac{5}{3} 4 . \tan θ = \frac{4}{3} 5 . c o t θ = \frac{3}{4}$

Step by step solution

Step 1 Given expression is,

$\sin θ = \frac{4}{5}$ .

Let $P = (x, y)$ is a point on the circle that corresponds to $θ$ . Since $\sin θ = \frac{4}{5} > 0$ and the angle $θ$ is acute , therefore the point $P$ lies in the first quadrant.

Step 2 Let us consider y=4,r=5.

So, the point $P (x, 4)$ corresponds to $θ$ lies on the circle of radius $5$ .

$x^{2} + 4^{2} = 5^{2} x^{2} + 16 = 25 x^{2} = 25 - 16 x^{2} = \sqrt{9} x = \pm 3$

Step 3 Since Px,y lies in the first quadrant, we take y=4,x=3,r=5.

$c s c θ = \frac{r}{y} = \frac{5}{4} \cos θ = \frac{x}{r} = \frac{3}{5} s e c θ = \frac{r}{x} = \frac{5}{3} \tan θ = \frac{y}{x} = \frac{4}{3} c o t θ = \frac{x}{y} = \frac{3}{4}$

These are the remaining trigonometric functions of the given expression.

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In Problems 16–23, find the exact value of each of the remaining trigonometric functions.
$\sin θ = \frac{4}{5}, θ$ is acute.

Short Answer

Step by step solution

Step 1 Given expression is,

Step 2 Let us consider y=4,r=5.

Step 3 Since Px,y lies in the first quadrant, we take y=4,x=3,r=5.

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In Problems 16–23, find the exact value of each of the remaining trigonometric functions.sinθ=45,θis acute.

Short Answer

Step by step solution

Step 1 Given expression is,

Step 2 Let us consider y=4,r=5.

Step 3 Since Px,y lies in the first quadrant, we take y=4,x=3,r=5.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Pure Maths

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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.
$\sin θ = \frac{4}{5}, θ$ is acute.