Trigonometric ratios:
- sine θ = perpendicular/hypotenuse
- cosine θ = base/hypotenuse
- tangent θ = perpendicular/base
- cosecant θ = 1/sin θ (known as cosec θ)
- secant θ = 1/cos θ (known as sec θ)
- cotangent θ = 1/tan θ (known as cot θ)
- tan θ = sinθ/cosθ
- cot θ = cosθ/sinθ
- tanθ * cotθ = 1
Trigonometric identites:
a. sin^2 θ + cos^2 θ = 1
b. 1 + tan^2 θ = sec^2 θ
c. 1 + cot^2 θ = cosec^2 θ
Complementary Angles:
The angles θ and (90 - θ) are called are called complimentary angles.
Results on complimentary angles :
a. sin (90-θ) = cos θ
b. cos (90-θ) = sin θ
c. tan(90-θ) = cot θ
d. cosec(90-θ) = sec θ
e. sec(90-θ) = cosec θ
f. cot(90-θ) = tan θ
Trigonometric ratios of Some particuar angles:
- θ sinθ cosθ tanθ cosecθ secθ cotθ
- 0 1 0 not defined 1 not defined
- 30 1/2 sqrt3/2 1/sqrt3 2 2/sqrt3 sqrt3
- 45 1/sqrt2 1/sqrt2 1 sqrt2 sqrt2 1
- 60 sqrt3/2 1/2 sqrt3 2/sqrt3 2 1/sqrt3
- 90 1 0 not defined 1 not defined 0
- -θ -sinθ cosθ -tanθ -cosecθ secθ -cotθ
- (90-θ) cosθ sinθ cotθ secθ cosecθ tanθ
- (90+θ) cosθ -sinθ -cotθ secθ -cosecθ -tanθ
- (180-θ) sinθ -cosθ -tanθ cosecθ -secθ -cotθ
- (180+θ) -sinθ -cosθ tanθ -cosecθ -secθ cotθ
Sum Formulae:
- sin (A+B) = sinA.cosB + cosA.sinB
- sin (A-B) = sinA.cosB - cosA.sinBc.
- cos (A+B) = cosA.cosB - sinA.sinB
- cos(A-B) = cosA.cosB + sinA.sinB
- tan (A+B) = (tanA + tanB) / (1- tanA tanB)f. tan (A-B) = (tanA - tanB) / (1+ tanA.tanB)
- cot(A+B) = (cotA.cotB - 1) / (cotB + cotA)
- cot(A-B) = (cotA.cotB +1) / (cotB - cotA)
- sin(A+B) . sin(A-B) = sin^2 A - sin^2 B = cos^2 B - cos^2 A
- cos(A+B) . cos(A-B) = cos^2 A - sin^2 B = cos^2 B - sin^2 A
- tan(A+B+C) = (tanA + tanB + tanC - tanA.tanB.tanC) / (1 - tanA.tanB - tanB.tanC - tanC.tanA)
Triple angle formulae:
- Sin3A = 3sinA - 4sin^3A
- Cos3A = 4cos^3A - 3cosA
- Tan3A = (3tanA - tan^3A) / (1-3tan^2A)
NOTE:
- pie = 22/7 = 3.1416
&
- 1/pie = 7/22 = 0.31831