Trigonometry
Trigonometric Ratios in a Right Triangle
Defines the fundamental trigonometric ratios in terms of the sides of a right-angled triangle.
Arc Length Formula
Gives the arc length subtended by an angle theta in radians at the centre of a circle of radius r.
Sine-Cosine Pythagorean Identity
Relates the squares of sine and cosine for any angle theta.
Secant-Tangent Pythagorean Identity
Relates tangent and secant of an angle for all angles where they are defined.
Cosecant-Cotangent Pythagorean Identity
Relates cotangent and cosecant of an angle for all non-multiple of pi angles.
Cofunction Identities for Complementary Angles
Expresses the trigonometric ratios of a complementary angle in terms of cofunctions.
Sine of Sum and Difference
Expands the sine of the sum or difference of two angles.
Cosine of Sum and Difference
Expands the cosine of the sum or difference of two angles.
Tangent of Sum and Difference
Expands the tangent of the sum or difference of two angles.
Cotangent of Sum and Difference
Expands the cotangent of the sum or difference of two angles.
Sine Double Angle Formula
Expresses sine of double angle in terms of single-angle trigonometric functions.
Cosine Double Angle Formula
Expresses cosine of double angle in terms of single-angle functions.
Tangent Double Angle Formula
Expresses tangent of double angle in terms of tangent of single angle.
Sine Triple Angle Formula
Expresses sine of triple angle as a cubic polynomial in sin theta.
Cosine Triple Angle Formula
Expresses cosine of triple angle as a cubic polynomial in cos theta.
Tangent Triple Angle Formula
Expresses tangent of triple angle in terms of tan theta.
Sum and Difference of Sines (C-D Formulas)
Transforms a sum or difference of two sines into a product of sine and cosine.
Sum and Difference of Cosines (C-D Formulas)
Transforms a sum or difference of two cosines into a product of cosines or sines.
Product-to-Sum Formulas
Converts products of sine and cosine functions into sums or differences.
Range of a sin x + b cos x
Gives the minimum and maximum possible values of any linear combination of sine and cosine.
General Solution of sin θ = sin α
Gives the complete set of solutions for a sine trigonometric equation.
General Solution of cos θ = cos α
Gives the complete set of solutions for a cosine trigonometric equation.
General Solution of tan θ = tan α
Gives the complete set of solutions for a tangent trigonometric equation.
Law of Cosines
Relates the cosine of an interior angle of a triangle to its three sides.