How to find the coordinates of a trigonometric function (5pi/2)?

Question

Hi, I'm assigned to find the six trigonometric functions for a whole list of degrees and radians, but I can't figure out how to find the coordinates of a given degree or radian. For example, with 5pi/2, how do I get the "a" and "b" (I know how to get the r once I get the a and b)?

Thanks! 10 points for best answer!

Answer 1

you can't do this by drawing a triangle as such (I assume that is what you mean by finding a,b,r) ... 5pi/2 is > pi and the total of the angles in a triangle add up to pi!

you can use basic rules
anyfunction(x+2pi) = thatfunction(x)
sin(x+pi) = -sinx = sin(-x)
cos( -x) = cos(x) = -cos(pi-x)

for 5pi/2 = pi/2 + 2pi
sin 5pi/2 = sin pi/2 = 1
cos 5pi/2 = cos pi/2 = 0
tan is indeterminate (oo)
inverse are
csc = 1/sin = 1/1 = 1
sec = 1/cos = indeterminate
cot = cos/sin = 0

Answer 2

Hi. I figured that since 5pi/2 is equal to 15pi/6, its coordinates are similar to those of pi/2. So the coordinates of 5pi/2 are x=0, and y=1. The x would be the cosine value and y would be the sine value.

If you're really that confused, you can try drawing a circle and cut them into 4 parts.

pi/6: x=(squareroot of 3)/2, y=1/2
pi/3: x=1/2, y=(squareroot of 3)/2
the four ones in the NEWS directions are simple enough.
for the other functions, you just change the signs of the values that are on the opposite side(left/right, up/down)

I hope that helped! gotta go

PS. if you're still confused, you can go over to wikipedia and type in 'trigonometric functions'. There is a complete diagram there.

Answer 3

X = cos(Angle)
Y = sin(Angle)
---------------------------------
Pi/2 = 90 degrees
5 Pi/2 = 5*90 degrees, but 4 *90 is once around
so cos(5Pi/2) = cos(Pi/2) = 0
sin(5Pi/2) = sin(Pi/2) = 1

Answer 4

The angle is NOT enough to find out the coordinates..You must have r or a or b.