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

Given information

Given point $(- 2, 5)$

Calculate the radius for circle at origin

Calculating, we get

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

Calculating the sine value

Here

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

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

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

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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

Step by step solution

Given information

Calculate the radius for circle at origin

Calculating the sine value

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Short Answer

Step by step solution

Given information

Calculate the radius for circle at origin

Calculating the sine value

One App. One Place for Learning.

Most popular questions from this chapter

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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 $t$ .