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Unit circle and trig. functions – About -pg. 1/7

Posted in Math Theory by Lia on 05/23/2017

Unit circle and trig. functions : pg. 1, 234, 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 circleunit circle, is the circle used in trigonometry, that has the radius equal with ( 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.

trigonometry chart_positive alpha

Below are the charts of sine and cosine for negative angles.

trigonometry chart_negative alpha

 

 

 

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).

 

Trig unit and trig functions signs

Unit circle and trig. functions : pg. 1, 234, 5, 6, 7

 

 

 

 

 

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