trigonomerty

• Trigonometric Basics   






sinθ=opposite sidehypotenuse=yr

cosθ=adjacent sidehypotenuse=xr

tanθ=opposite sideadjacent side=yx

cscθ=hypotenuseopposite side=ry

secθ=hypotenuseadjacent side=rx

cotθ=adjacent sideopposite side=xy



From Pythagorean theorem, x2+y2=r2 for the right angled triangle mentioned above



• Basic Trigonometric Values   

θ in degrees	θ in radians	sinθ	cosθ	tanθ
0°	0	0	1	0
30°	π6	12	3√2	13√
45°	π4	12√	12√	1
60°	π3	3√2	12	3√
90°	π2	1	0	Not defined
180°	π	0	-1	0
270°	3π2	-1	0	Not defined
360°	2π	0	1	0




• Trigonometric Formulas   

Degrees to Radians and vice versa

360°=2π radian


Trigonometry Quotient Formulas

tanθ=sinθcosθ

cotθ=cosθsinθ



Trigonometry - Reciprocal Formulas

cscθ=1sinθ

secθ=1cosθ

cotθ=1tanθ



Trigonometry - Pythagorean Formulas

sin2θ+cos2θ=1

sec2θ−tan2θ=1

csc2θ−cot2θ=1



Trigonometry - Even-Odd Formulas

sin(−θ)=−sinθ

cos(−θ)=cosθ

tan(−θ)=−tanθ

csc(−θ)=−cscθ

sec(−θ)=secθ

cot(−θ)=−cotθ



Trigonometry - Periodic Formulas

if n is an integer,

sin(θ+2πn)=sinθ

cos(θ+2πn)=cosθ

tan(θ+2πn)=tanθ

csc(θ+2πn)=cscθ

sec(θ+2πn)=secθ

cot(θ+2πn)=cotθ

(In these formulas, θ is mentioned in radians. If θ is in degrees, substitute 360° for 2π)