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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 6: Q. 46 (page 435)

Find the exact value of $\sin t, \cos t$ , and $\tan t$ if $P = (- 2, 5)$ is the point on the circle that corresponds to $t$ .

Short Answer

Expert verified

The value of $\sin t, \cos t, \tan t$ is $\frac{5 \sqrt{29}}{29}, - \frac{2 \sqrt{29}}{29}, - \frac{5}{2}$ respectively

Step by step solution

01

Given information

Given point $(- 2, 5)$

02

Calculate the radius for circle at origin

Calculating, we get

$r = \sqrt{x^{2} + y^{2}} r = \sqrt{- 2^{2} + 5^{2}} r = \sqrt{4 + 25} r = \sqrt{29}$

03

Calculating the sine value

Here

$\sin t = \frac{y}{r} \sin t = \frac{5}{\sqrt{29}} 路 \frac{\sqrt{29}}{\sqrt{29}} \sin t = \frac{5 \sqrt{29}}{29}$

$\cos t = \frac{x}{r} \cos t = \frac{- 2}{\sqrt{29}} 路 \frac{\sqrt{29}}{\sqrt{29}} \cos t = - \frac{2 \sqrt{29}}{29}$

$\tan t = \frac{\sin t}{\cos t} \tan t = \frac{\frac{5 \sqrt{29}}{29}}{- \frac{2 \sqrt{29}}{29}} \tan t = - \frac{5 \sqrt{29}}{29} 路 \frac{29}{2 \sqrt{29}} \tan t = - \frac{5}{2}$

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