24The point P in the figure below has y-coordinate25yAP1 xFind the following.(а)sin t(b)Cos t(c)tan t(d)sec t

Name: 24The point P in the figure below has y-coordinate25yAP1 xFind the fo
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Description: 24The point P in the figure below has y-coordinate25yAP1 xFind the following.(а)sin t(b)Cos t(c)tan t(d)sec t

Answered: Find the following. (a) sin t (b) cos t…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

24
The point P in the figure below has y-coordinate
25
yA
P
1 x
Find the following.
(а)
sin t
(b)
Cos t
(c)
tan t
(d)
sec t

Expert Solution

Step 1

It is known that in a unit circle, $x^{2} + y^{2} = 1$ where r=1.

It is given that the y coordinate is $\frac{24}{25}$ .

Evaluate the x coordinate as follows.

$x^{2} + y^{2} = 1 x = \sqrt{1 - y^{2}} x = \sqrt{1 - {(\frac{24}{25})}^{2}} x = \sqrt{\frac{25^{2} - 24^{2}}{25^{2}}} x = \pm \frac{7}{25}$

Since the point P is in second quadrant, the x coordinate is $x = - \frac{7}{25}$ .

Step 2

(a)

Evaluate sin t as follows.

$\begin{array}{rcl} \sin t & = & \frac{y}{r} \\ = & \frac{(\frac{24}{25})}{1} \\ = & \frac{24}{25} \end{array}$

Thus, $\sin t = \frac{24}{25}$ .

Step 3

(b)

Evaluate cos t as follows.

$\begin{array}{rcl} \cos t & = & \frac{x}{r} \\ = & \frac{(- \frac{7}{25})}{1} \\ = & - \frac{7}{25} \end{array}$

Thus, $\cos t = - \frac{7}{25}$ .

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