Circular Functions

Unit Circle

A circle with a radius of 1, centred at the origin​. Circumference = 2π

Radian (Rad/C)

A unit of angle measure based on arc length

Degree

A unit used to measure distances around a circle. One degree equals 1/360 of a full circle.

Degree - Radian

1° = π/180 (Rad)

Radian - Degree

1 Rad = 180°/π (Degree)

Exact Values

X/Y Functions

x = cos θ
y = sin θ

P(θ) =

( Cos θ, Sin θ )

Tan θ =

sin θ/cos θ (O/A)

Sin θ =

opposite/hypotenuse (O/H)

Cos θ =

adjacent/hypotenuse (A/H)

Unit Circle Quadrants

ASTC
1 = All
2 = Sine
3 = Tangent
4 = Cosine

Amplitude (a)

The maximum or minimum values of sin/cos x. Change results in dilation in the y-axis. Range = [-a, a]

Period (2π/n)

The horizontal interval between the repetitions (wavelength) Change results in dilation in the x-axis.

Cos Graph

Starts at 1

Sin Graph

Starts at 0

Solve Equations

1st Solution is obtained through exact values, 2nd symmetry and the rest = +/-2π

Y = a sin/cos n (t ± ε) Translation

The graph is translated in '± ε' units in the x-axis

Y = a sin/cos n (t ± ε) ± B Translation

The graph is translated ± B in the y-axis

Sin /(π/2 - θ)

= Cos θ

Cos (π/2 - θ)

= Sin θ

Sin (π/2 + θ)

= Cos θ

Cos (π/2 + θ)

= -Sin θ

Pythagorean Identity

sin²θ + cos²θ = 1

Sin π/2

0

Cos π/2

0

Sin π/3

√3/2

Cos π/3

1/2

Sin π/4

√2/2 / 1/√2

Cos π/4

√2/2 / 1/√2

Sin π/6

1/2

Cos π/6

√3/2

Tan Graph

Tan Asymptote Formula

(2k+1)π/2 = x

Tan Period & Range

π & R

Tan π/6

√3/3

Tan π/4

1

Tan π/3

√3

Tan π/2

Undefined

Tan π

0