This article is specially for those who wants to learn basics of trigonometry.This article will make you learn about different trigonometric formulas which are used in calculations.
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.
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.
Sinθ = 1/Cosecθ
Cosθ = 1/Secθ
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
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