Trigonometric Functions

Hope all of you know about the Right angled triangle where one angle is 90 degree and other two angles collectively make angle of 90 degree. In this triangle names of the sides areperpendicular, base and hypotenuse.

A |\

|   \

|      \

C | ____\B

In the above diagram side AB is hypotenuse , side CB is base and last but not the least side AC is perpendicular.Side AC is perpendicular t side CB

1. Sinθ = Perpendicular / Hypotenuse

2. Cosθ = Base / Hypotenuse

3. Tanθ= Perpendicular / Base

4. Coseineθ = Hypotenuse/Perpendicular

5.Secantθ = Hypotenuse/Base

6.Cotθ = Base/Perpendicular

All of us know that there are four quadrants in 360 degrees as followed:

0 to 90 degrees = first quadrant

90 to 180 degrees = second quadrant

180 to 270 degrees = third quadrant

270 to 360 degrees = fourth quadrant

Now let see the signs of all trigonometric functions in these quadrants:

1. All trigonometric functions are positive in Ist quadrant.

2. Only sin and cosec are positive in second quadrant rest are negative.

3. Only Tan and Cot are positive in third quadrant rest are negative.

4. Only Cos and Sec are positive in fourth quadrant rest are negative.

Basic formulaes:

Sinθ = 1/Cosecθ

Cosθ = 1/Secθ

Tanθ= 1/Cotθ

similarly:

Cosecθ = 1/Sinθ

Secθ = 1/Cosθ

Cotθ = 1/Tanθ

when conversion of functions face 90 degree or 270 degree then :

Sinθ changes into cosθ

cosθ changes into Sinθ

cosecθ changes into Secθ

secθ changes into Cosecθ

Tanθ changes into Cotθ

Cotθ changes into Tanθ

while if conversion face 180 or 360 degrees then the functions remains the same.

Sin2θ + Cos2θ = 1

Cosec2θ - cot2θ = 1

Sec2θ - tan2θ = 1