Question

How does the unit circle help you in graphing the trigonometric functions on the cartesian plane?

Answer 1

The trig unit circle with origin O, radius unity, has 4 axis that define the 4 common trig functions. When an variable Arc AM that rotates counterclockwise on the trig circle:
The horizontal AOx defines the fucntion f(x) = cos x. When the arc AM varies from 0 to 2Pi, the function f(x) varies from 1 to -1 , then back to 1.
The vertical axis OBy defines the function f(x) = sinx
The vertical axis AT defines the function f(x) = tan x.
The horizontap BZ defines the function f(x) = cot x.
Graphing trig functions on the cartesian plane .
Example . Graph the function f(x) = cos x. This is a periodic function with period 2Pi.
The domain goes from 0 to 2Pi, passing at values Pi/4; Pi/2, 2Pi/; Pi;
4Pi/3; 3Pi/2; 5Pi/3; and 2Pi.
The range goes from 1 (x = 0), to 0 (x = Pi/2), to -1 (x = Pi) then back to 1 (x = 2Pi).
These values help to draw the graph of f(x) = cos x.
Some additional values of f(x) corresponding to x = Pi/4, Pi/3, ,,,,,5Pi/3 gives a few more accurate details of the graph.