Trigonometry Quadrants

 Trigonometry is a part of mathematics in which it studies about triangles, mainly right triangles. Trigonometry deals with relationships between the angles and sides of triangles and also with the trigonometric functions. Here, we are study about the trigonometry quadrants.

 

There are four types of trigonometry quadrants available in trigonometry.

  • Quadrant I is from 0 to 90 degrees = 0 to p/2 radians
  • Quadrant II is from 90 to 180 degrees = p/2 to p radians
  • Quadrant III is from 180 to 270 degrees = p to 3p/2 radians
  • Quadrant IV is from 270 to 360 degrees = 3p/2 to 2p radians

Where p = 3.14 rounded to 2 decimal places.

 

Examples

 

Example 1: Find sin (273o).

            Solution:

Sin (273) = sin (270 + 3)

= sin (270) cos (3) + cos (270) sin (3)

= (-1)cos(3)

= - 0.989

Example 2: Find the angle ‘a’ if sin (a) = -0.026551154 and cos (a) = -0.999647456

Solution:

Here, the sine is (+)ve and the cosine is (-)ve, we know the angle is in quadrant II which means the angle is between 90o and 180o.

sin (a) = -0.026551154           and       cos (a) = -0.999647456         

a = Sin -1(-0.026551154)        and       a = cos -1(-0.999647456)      

a= 66                                    and       a = 66

Sin (66) = -0.026551154 and cos (66) = -0.999647456, and cos(114) =-0.999647456.

sin(114) = sin(180 - 66)
             = sin(180)cos(66) - cos(180)sin(66)
             = 0*cos(66) - (-1)*sin(66)
             = sin(66)

Since sin (114) = sin (66), our angle is 114o 

Problems to find sign :

 

Example3: What is the sign (+ or - ?) of:

A. cos 105°

b. sin 40°

c. csc 310°

Do these without calculator.

Solution:

a. Negative (100 degrees is in the second quadrant)

b. Positive (first quadrant - all are positive)

c. Negative (310 degrees is in the 4th quadrant)

Example4 : What is the sign (+ or -) of

a) sec (-25°)

c) cos(185°)    

Solution:

a. Positive (-25 degrees is in the 4th quadrant, since negative angles are measured clockwise.)

c. Negative (185 degrees is in the 3rd quadrant, and cos is negative there.