Trigonometry and Polar Coordinates Flashcards

Flashcards for trigonometry and polar coordinates.

Six Primary Trigonometric Functions

Sine, cosine, tangent, cosecant, secant, and cotangent.

Inverse Trig Functions

arcsin(x), arccos(x), arctan(x)

Reciprocal Trig Identities

csc(θ) = 1 / sin(θ), sec(θ) = 1 / cos(θ), cot(θ) = 1 / tan(θ)

General Form of a Polar Equation

r = f(θ)

Common Types of Polar Graphs

Circles, Lines, Limacons, Rose curves, Spirals

Period of sin(x) or cos(x)

Period = 2π / |B| in y = A sin(Bx) or y = A cos(Bx)

Period of tan(x) or cot(x)

Period = π / |B| in y = A tan(Bx) or y = A cot(Bx)

Converting from Polar to Rectangular Coordinates

x = r cos(θ), y = r sin(θ)

Converting from Rectangular to Polar Coordinates

r = √(x² + y²), θ = tan ⁻¹(y / x)

Convert Complex Number (Polar to Rectangular)

If z = r(cosθ + i sinθ), then z = r cis(θ) = r cos(θ) + i r sin(θ)

Convert Complex Number (Rectangular to Polar)

Given z = a + bi: r = √(a² + b²), θ = tan ⁻¹(b / a); Then z = r cis(θ)

Sine Function

sin(θ) = opposite / hypotenuse

Cosine Function

cos(θ) = adjacent / hypotenuse

Tangent Function

tan(θ) = opposite / adjacent