Thread: What is the value of cos(pi + 301pi/2)

1. What is the value of cos(pi + 301pi/2)

I have to make a video explaining this problem, sent by the person who hired me, but it doesn't appear to be correct.

What is the value of cos( + 301/2)?
A.-1/2
B. 1
C. 0
D. 1/2
E 3/2

This is the solution given:

cos(+301/2) = cos(+75*2+ /2)= cos(+ /2)
= 0
Ans: C

When I use degrees = radians * 180/pi, that answer isn't correct. And when I plug in the original cos (pi+301pi/2) into google calculator, it isn't 0.

Am I missing something?

2. Originally Posted by fcabanski
I have to make a video explaining this problem, sent by the person who hired me, but it doesn't appear to be correct.

What is the value of cos( + 301/2)?
A.-1/2
B. 1
C. 0
D. 1/2
E 3/2

This is the solution given:

cos(+301/2) = cos(+75*2+ /2)= cos(+ /2)
= 0
Ans: C

When I use degrees = radians * 180/pi, that answer isn't correct. And when I plug in the original cos (pi+301pi/2) into google calculator, it isn't 0.

Am I missing something?
I assume you mean what is in the title?? not the ??

$\displaystyle \cos\left(\pi+ \frac{301\pi}{2}\right)=\cos\left(\frac{303\pi}{2} \right)$

Now cosine is a perioidic function with a period of two pi i.e

$\displaystyle \cos(2\pi n +x)=\cos(x)$ where n is any integer.

so $\displaystyle \frac{303\pi}{2}=151\pi +\frac{\pi}{2}=150\pi +\frac{3}{2}\pi=2\pi (75)+\frac{3\pi}{2}$

so finally we get

$\displaystyle \cos \left( 150\pi +\frac{3\pi}{2}\right) =\cos \left(\frac{3\pi}{2}\right)=0$

3. Originally Posted by fcabanski

When I use degrees = radians * 180/pi, that answer isn't correct. And when I plug in the original cos (pi+301pi/2) into google calculator, it isn't 0.

Am I missing something?

$\displaystyle \frac{301\pi}{2}\cdot\frac{180}{\pi}=27090$ degrees.

$\displaystyle \cos\left(\pi+\frac{301\pi}{2}\right)\Longrightarr ow \cos(180+27090)=0$

4. Thanks.

I know your explanation is correct. However, why does Google calculator get it wrong when I enter:

cos (pi+301pi/2)?