Trigonometry involves the study of relationships between angles and sides of triangles. Here are some important trigonometric formulas that are commonly used.
Most Important Trigonometric Formula for class 9, 10, 11, 12
Last Updated On: 12 August 2023
Certainly! Trigonometry involves the study of relationships between angles and sides of triangles. Here are some important trigonometric formulas that are commonly used:
Ratios of Angles:
Sine (sin): Opposite / Hypotenuse
Cosine (cos): Adjacent / Hypotenuse
Tangent (tan): Opposite / Adjacent
Reciprocal Trigonometric Ratios:
Cosecant (csc): 1 / sin
Secant (sec): 1 / cos
Cotangent (cot): 1 / tan
Pythagorean Trigonometric Identity:
sin^2(θ) + cos^2(θ) = 1
Quotient and Reciprocal Identities:
Cotangent in terms of Tangent: cot(θ) = 1 / tan(θ)
Secant in terms of Cosine: sec(θ) = 1 / cos(θ)
Cosecant in terms of Sine: csc(θ) = 1 / sin(θ)
Co-Function Identities:
Cofunction of Sine: cos(90° - θ) = sin(θ)
Cofunction of Cosine: sin(90° - θ) = cos(θ)
Cofunction of Tangent: cot(90° - θ) = tan(θ)
Sum and Difference Formulas:
Sine of Sum: sin(A + B) = sin(A)cos(B) + cos(A)sin(B)
Cosine of Sum: cos(A + B) = cos(A)cos(B) - sin(A)sin(B)
Double Angle Formulas:
Sine of Double Angle: sin(2θ) = 2sin(θ)cos(θ)
Cosine of Double Angle: cos(2θ) = cos^2(θ) - sin^2(θ) = 2cos^2(θ) - 1 = 1 - 2sin^2(θ)
Half Angle Formulas:
Sine of Half Angle: sin(θ/2) = ±√((1 - cos(θ)) / 2)
Cosine of Half Angle: cos(θ/2) = ±√((1 + cos(θ)) / 2)
Product-to-Sum Formulas:
Sine of Difference: sin(A - B) = sin(A)cos(B) - cos(A)sin(B)
Cosine of Sum: cos(A + B) = cos(A)cos(B) + sin(A)sin(B)
These are just some of the fundamental trigonometric formulas that you'll encounter. Understanding these formulas and how to apply them in different contexts will greatly help in solving trigonometry problems.