Trig Question...

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

is there an easy way to do this besides converting to degrees?

hm..this one is tough
cos(303pi / 2)
pie is 180 so if we have odd number multiplied, it will always be at x= -1 position.
but we divide it by two so it's at x = 0 position
is the answer 0?

This is actually really easy! First look at 301pi/2. Every time you go around the unit circle, it is 2pi right? For instance 6pi is the same as 2pi. 10pi is the same as 2pi. 301pi is the same as pi. Divide it by 2 and you get pi/2. Add the other pi and you get 3pi/2. That's like going around the unit circle 3/4 of the way. Since it's Cos, you find the x coordinate at that position which is 0.

This is actually really easy! First look at 301pi/2. Every time you go around the unit circle, it is 2pi right? For instance 6pi is the same as 2pi. 10pi is the same as 2pi. 301pi is the same as pi. Divide it by 2 and you get pi/2. Add the other pi and you get 3pi/2. That's like going around the unit circle 3/4 of the way. Since it's Cos, you find the x coordinate at that position which is 0.

Be careful... 301pi is like pi, but it doesn't follow FROM THAT that 301pi/2 is like pi/2.

If you had 303pi you could say that was similar to pi but 303pi/2 is actually similar to 3pi/2.

You just need to realize that 301pi/2 is 300pi/2 + pi/2 and that 300pi/2 is 150pi and that 150pi is in the form of 2n(pi) which means you've just looped around the circle 75 times. So 301pi/2 is a fancy way of saying pi/2.

Ah so the safe way to do it would be to divide the 2 before factoring out all the 2pis. So 301pi/2 is 150.5pi or pi/2
303pi/2 would be 151.5pi which would reduce to 1.5pi or 3pi/2. Thanks for catching that.

so was I right and the answer is 0? I don't know why but when I use the calculator T83, it doesn't give me 0. I changed back and forth between radian and degree but it never gives me 0. hm...

All you guys are right... but what you guys are missing is that you are adding the pi with the 301/2pi.... you can do that.... i see this similar problem on the Crack the Math.... what you do is do each trig function seprately and then add those numbers together.
So....
The answer for Cos (pi + 301/2pi) would be...
= Cos(pi) + cos(301/2 pi)
= -1+ cos(pi/2)
= -1+0
= -1

All you guys are right... but what you guys are missing is that you are adding the pi with the 301/2pi....

isn't it why we all got 303pi/2 ?

All you guys are right... but what you guys are missing is that you are adding the pi with the 301/2pi.... you can do that.... i see this similar problem on the Crack the Math.... what you do is do each trig function seprately and then add those numbers together.
So....
The answer for Cos (pi + 301/2pi) would be...
= Cos(pi) + cos(301/2 pi)
= -1+ cos(pi/2)
= -1+0
= -1

That's absolutely incorrect. You can't just break up the angle like that.
Example:
0=Cos(pi/2)=Cos(0+pi/2)= cos(0) + cos(pi/2) = 1+0 = 1???? I think not ;p

0 is the right answer. Cos(303pi/2)=cos(2pi*150+3pi/2)=cos(3pi/2)=0

All you guys are right... but what you guys are missing is that you are adding the pi with the 301/2pi.... you can do that.... i see this similar problem on the Crack the Math.... what you do is do each trig function seprately and then add those numbers together.
So....
The answer for Cos (pi + 301/2pi) would be...
= Cos(pi) + cos(301/2 pi)
= -1+ cos(pi/2)
= -1+0
= -1
Someone said it but here's how you do that really:

cos(x + y) = cos(x)cos(y) - sin(x)sin(y)

cos(pi + 301pi/2) = cos(pi)cos(301pi/2) - sin(pi)sin(301pi/2)

Since sin(pi) = 0 the second term disappears and we're left with the first term.

cos(301pi/2) is the same as cos(pi/2) which is 0 so the answer is 0.