# Trigonometric Ratios and and Special Angles

• Nov 28th 2009, 06:26 PM
darksoulzero
Trigonometric Ratios and and Special Angles
Use the unit circle to determine exact values of the primary trigonometric ratios for each angle

A) (3pi)/2 B) pi

I dunno wth is going on, but those don't give me a special triangle, can someone explain this? Also, how do I put my math in math form?

• Nov 28th 2009, 07:59 PM
I<3Kinematics
Quote:

Originally Posted by darksoulzero
Use the unit circle to determine exact values of the primary trigonometric ratios for each angle

A) (3pi)/2 B) pi

I dunno wth is going on, but those don't give me a special triangle, can someone explain this? Also, how do I put my math in math form?

ok so it is asking for you to find sine cosine tangent cotangent etc. for these two places on the unit circle. <as i understand your question>
so we know that the cosine is the best friend of the x part of a coordinate of a point on the unit circle and that the sine is the best friend of the y part of a coordinated of a point on the unit circle so if a point were to be on the x axis and be (1,0) the cosine of that point (which is technically called 2 pi ) would be 1 and the sine would be 0.

using the unit circle we know a few things such as that the positive side of the x axis can be called zero or 2 pi or any multiple thereof, the pos y axis is called (1/2)pi, neg x is called pi, neg y is called (3/2) pi.

from there using the x and y coordinates for cosine and sine and using the trig identities such as tan=sine/cosine to find out the rest

(keep in mind the coordinates for those four either have to be (1,0) (0,1) (-1,0) (0,-1) going counter-clockwise from the pos x axis) (Happy)
• Nov 29th 2009, 01:47 PM
darksoulzero
But wait a minute, how is it possible to have a sin or cos of a straight line? That is, if a point P is placed on the unit circle with a set of coordinates of (1,0) how can it have an angle if it's just a line?
• Dec 2nd 2009, 04:22 AM
satis
Quote:

Originally Posted by darksoulzero
But wait a minute, how is it possible to have a sin or cos of a straight line? That is, if a point P is placed on the unit circle with a set of coordinates of (1,0) how can it have an angle if it's just a line?

It's an angle of 0 degrees. For instance, take a point on the right side of the graph on the x axis at 0,1. The hypotenuse is 1, the adjacent side is 1 (they're both the same thing), and the opposite side is 0. thus sin = 0/1, cos = 1/1, tan = 0/1, csc = 1/0 (undefined), sec = 1/1, and cot = 1/0 (undefined).