Math (Trig)
posted by Chris .
I have a unit circle graph like the one at the top of a website (do a google search for 'unit circle trig functions' and click the second link, since I can't post links).
I need to label the sine, cosine, tangent, secant, cosecant, and cotangent. I found several pictures that show the answers, but not how to arrive at them. How can I show work for this problem?
The figure I see at the link http://www.clarku.edu/~djoyce/trig/
labels sin, cos, tan and cot as lengths relative to a circle with a radius of 1, for the angle defined in green. All you should need to understand it is the definitions of sin, cos, tan and cot and the fact that the radius of the circle is 1.
The secant (which is not shown in the figure) is the length of the line from the center to the point where the blue "tan" line meets the diagonal.
Thanks for your help, that's the figure I was talking about. I'm still confused though as to how I would show work for the problem. I know sine = opposite * adjacent and stuff, but I don't see how sin / cos would tell me that the blue line specifically is the tangent.
The blue line's length represents the tangent because it is perpendicular to a horizontal radius line of length 1. (All radii are 1 because it is a "unit circle".) Note the right triangle that the "tan" line forms with the horizontal radius line and the diagonal line from the center to the blue dot.
tan/1 is, by definition, the tangent of the blueshaded angle.
If I may add the last trig ratio.
The length of the rotating arm to the end of the yellow part show would be the cosecant.
Several years ago a student made such a model for a math project. It was so well constructed that I was able to use it to demonstrate the trig ratios for many years.
I donated the model to our math department upon my retirement.
Respond to this Question
Similar Questions

trig
I have no idea how to solve this problem. <A is in standard position on a unit circle. Point P (1/2, √3/2) is the point of intersection of its terminal side with the unit circle. Find the measure of <A in radians. 
Trig
Does anybody know a good website that will help me with finding the six trig functions of a point NOT on the unit cricle? 
Math Trig
At what two points on the unit circle is the xcoordinate equal to the ycoordinate? 
Trig
Solve: 3tan^2x1=0. I got +/ (the sq. root of 3)/3 which is correct according to my study guide. However, I don't know how to use the unit circle to find this. The copy of the unit circle which I have does not have tangent values … 
trig
use the unit circle to find the exact value for all the trig functions of è=2ð/3. 
math
correction: use the unit circle to fin the ecaxtvalue for all trig functions theta=2pi/3 
trig question
On a unit circle, sin x = square root 3 over 2, with center O. Vertical line from top to center of circle is PO. Horizontal line from middle to right of circle is OE. Another vertical line of AB is parallel to PO. And radius of circle … 
trig question
NEW DIAGRAM: On a unit circle, sin x = square root 3 over 2, with center O. Vertical line from top to center of circle is PO. Horizontal line from middle to right of circle is OE. Another vertical line of AB is parallel to PO. And … 
trig
Let be an angle in standard position and the point (a, b) be the point of intersection of the terminal side of with the unit circle. State the unit circle definitions of the six trigonometric functions. cos = sec = sin = csc … 
trig
i have to draw a flat unit circle all the way to 4 pi in radians. i can get to 2 pi but i have trouble finding the radians if i went one more time around the unit circle.