Unit circle and trig. functions – About pg. 1/7
Unit circle and trig. functions : pg. 1, 2, 3, 4, 5, 6, 7
Contents:
pg.1…..Unit circle and trig. functions – About
pg.2…..Unit circle and trig. functions – Sine and cosine for
30° (π/6), demonstration.
pg.3…..Unit circle and trig. functions – Sine and cosine
for 45° (π/4), demonstration.
pg.4…..Unit circle and trig. functions – Sine and cosine
for 60° (π/3), demonstration.
pg.5…..Unit circle and trig. functions – Unit circle chart, for special angles.
pg.6…..Unit circle and trig. functions – Trig. functions for special angles.
pg.7…..Unit circle and trig. functions – Graphs for basic trig. functions.
1. About unit circle and trig. functions.
As mention in Angles and Unit circle – Unit circle, unit circle, is the circle used in trigonometry, that has the radius equal with 1 ( unit).
As shown in Right triangle and trigonometric functions:
If we consider the right triangle, , inside the unit circle (shown below), the hypotenuse of , OA = R = 1, therefore:

sin α = opposite leg = AB = OC (AB projection on y axis)

cos α = adjacent leg = OB (on x axis).
The charts below, are shown, the sine and cosine functions, for positive and negative angles, in standard position, having their terminal sides in different quadrants.
As can be seen the y axis is associated with cosine of an angle while the x axis is associated with sine of an angle.
Below are the charts of sine and cosine for positive angles.
Below are the charts of sine and cosine for negative angles.
Knowing the values and signs of sine and cosine for an angle and using the relationship between different trigonometric functions ( see Right triangle and trigonometric functions ) we can find out the values and signs for the other trigonometric functions (tangent, cotangent, secant and cosecant).
Below is the chart with the trigonometric functions and their sign (for angles that are in standard position with their terminal side in a specified quadrant).
Unit circle and trig. functions : pg. 1, 2, 3, 4, 5, 6, 7
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