AP Precalculus Terms

30 degrees

π/6

45 degrees

π/4

60 degrees

π/3

90 degrees

π/2

180 degrees

π

360 degrees

2π

Sin(π/6)

1/2

Tan(π/6)

2/√3

Cos(π/6)

√3/2

Sin(π/3)

√3/2

Cos(π/3)

1/2

Tan(π/3)

√3

Sin(π/4)

1/√2

Cos(π/4)

1/√2

Tan(π/4)

1

Formula for finding measure of Θ

Θ = s/r

Formula for finding sector length

s = rΘ

Cos0

1

Sine(90 degrees)

1

Cosine(90 degrees)

0

Tangent(90 degrees)

undefined

In a unit circle, sine is the ___ value

y

In a unit circle, cosine is the ___ value

x

Formula to convert radians to degrees

radians = degrees x (π/180)

Formula to convert degrees to radians

Degrees = radian measure x (180/π)

Sin(a+b)

sinAcosB + sinBcosA

Sin(a-b)

sinAcosB - sinAcosB

Cos (a+b)

cosAcosB - cosAcosB

Cos (a-b)

cosAcosB + sinAsinB

Sin(2a)

2sinAcosA

Cos(2a)

2cos^2a -1, 1-2sin^2a, cos^2a-sin^2a

Formula for finding r (radius from rectangular)

√x^2 +y^2

Formula for Θ (theta from rectangular)

tan^-1 (y/x)

Formula for x (polar to rectangular)

rcosΘ

Formula for y (polar to rectangular)

rsinΘ

Formula for complex equations

z = a + bi

Formula for r (rectangular to complex)

√a^2 + b^2

formula for Θ (rectangular to complex)

tan^-1 (b/a)

Formula for z (rectangular to complex)

rcosΘ + irsinΘ

Formula for x (complex to rectangular)

rcosΘ

Formula for y (complex to rectangular)

rsinΘ

Formula for z (complex to rectangular)

x + iy

Change of base formula for LogaB

LogcB/LogcA

Trig identities (sin)

sin^2 + cos^2 = 1

Trig identities (tan)

Tan^2 + 1 = sec^2

Trig identities (cot)

cot^2 + 1 = csc^2