Trigonometry Ratio, Angles/Radian and Quadrants

 Circle and Quadrants

So far, we have worked on the trigonometric value of acute angles. Let's look at angles beyond 90^o

Computation of X      

   2nd Quadrant : X = 180^o - y.   (where y = x in the first quadrant)

   3rd Quadrant : X = 180^o + y

   4th Quadrant = 360^o - y

For angles between 360^o and 720^o,

   1st Quadrant : X - 360^o

   2nd Quadrant : X = (180+360)^o - y  (where y = x in the first quadrant 360^o-540^o)

   3rd Quadrant : X = (180+360)^o - y 

   4th Quadrant :  X =  (360 + 360)^o - y

Angles beyond 720^o are calculated similarly

Degree and Radian (Unit of Measures) for angles
An angle can also be measured using radian as a unit of measure.
=> Both degree and radian is a measure of angle.

Radian is defined as the angle from the centre of a circle which intercepts an arc equal in length to the radius of the circle.

Both degree and radian is a measure of angle.

                  360^o = 2π rad

                 => 1^o = 2π rad / 360^o

  

         2π rad = 360^o

           =>   1 rad = 360^o / 2π

Converting between Degree and Radian

                  360^o = 2π rad

Example

What is the value of 240^o in rad?

    360^o = 2π rad

  240^o = 2π rad x 240^o

                 360^o

           = 4π/3 rad

Trigonometric Angles and Quadrants

SinX, CosX and TanX

First Quadrant : 0^o - 90^o 

All values of SinX, CosX and TanX are positive values.

Second Quadrant : 90^o - 180^o 

SinX has a positive value.

CosX and TanX have negative values.

Third Quadrant : 180^o - 270^o 

TanX has a positive value.

CosX and SinX have negative values.

Fourth Quadrant : 270^o - 360^o 

CosX has a positive value.

TanX and SinX have negative values.

The positive values for SinX, TanX and CosX can be remembered by:

         Quadrant:      1st     2nd      3rd    4th      

                               All Students Take Coffee

                                     I              A       O

                                    N             N       S