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.
Where p = 3.14 rounded to 2 decimal places.
Example 1: Find sin (273o).
Sin (273) = sin (270 + 3)
= sin (270) cos (3) + cos (270) sin (3)
= - 0.989
Example 2: Find the angle ‘a’ if sin (a) = -0.026551154 and cos (a) = -0.999647456
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)
Since sin (114) = sin (66), our angle is 114o
Example3: What is the sign (+ or - ?) of:
A. cos 105°
b. sin 40°
c. csc 310°
Do these without calculator.
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°)
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.