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Chapter 6: Q. 22 (page 437)

the point (x, y) is on the terminal side of angle $ϑ$ in standard position. Find the exact value of the given trigonometric function
$(2, 7), \sin ϑ$

Short Answer

Expert verified

$\sin ϑ = \frac{7}{\sqrt{53}}$

Step by step solution

01

Step 1. Given information

$(2, 7), \sin ϑ$

02

Step 2. Solving for sinϑ

We know that for any given point (x,y)

$\sin ϑ = \frac{y}{r} r = \sqrt{x^{2} + y^{2}}$

Using this :

$\sin ϑ = \frac{y}{r} \sin ϑ = \frac{7}{\sqrt{2^{2} + 7^{2}}} \sin ϑ = \frac{7}{\sqrt{53}}$

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Most popular questions from this chapter

True or FalseThe only even trigonometric function are the cosine and secant functions.

What is 1 radian? What is 1 degree?

In Problems $1 - 3$ , convert each angle in degrees to radians. Express your answer as a multiple of $π$ .

$1 . 260 °$

In problems 13-20, $P (x, y)$ is the point on the unit circle that corresponds to a real number $t$ . Find the exact values of the six trigonometric functions of $t$ .

$(- \frac{\sqrt{5}}{3}, - \frac{2}{3})$ .

In problems 13-20, $P (x, y)$ is the point on the unit circle that corresponds to a real number $t$ . Find the exact values of the six trigonometric functions of $t$ .

$(- \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2})$ .

See all solutions

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