How do you memorize the unit circle?
3 Answers
Look at the various ratios given on the unit circle and observe the symmetry in the values of sin, cos and tan. Once one understands it, the values would come to mind automatically
There's rather a lot to memorise. Best to start with simple angles and make sure you know those first, but there are many more that you can memorise if you want to.
Explanation:
The trig unit circle.
Explanation:
It is an oriented circle with radius R = 1. The variable arc AM rotates counterclockwise on the trig unit circle. The measure of the trig arc AM is the measure of the central angle <AOM. As a consequence, all trig functions of the angle <AOM are exactly the same as the trig
functions of the arc AM = x.
By convention, general trigonometry studies the variation of the arc AM = x rotating on the trig unit circle, and not the variation of the central angle <AOM.
The 4 main trig functions, f(x) = sin x, f(x) = cos x, f(x) = tan x and f(x) = cot x are the projections of the arc AM = x on the 4 different axis of the trig unit circle.
a. f(x) = sin x is the projection on the horizontal axis OAx.
b. f(x) = cos x is the projection on the vertical axis OBy
c. f(x) = tan x is the projection on the vertical axis AT
d. f(x) = cot x is the projection on the horizontal axis BU
