AP Precalc Exam Study

even and odd functions

• f(-x) = f(x)

• f(-x) = -f(x)

polynomial function end behaviors

VA

what would make the denominator 0 once the function is simplified

pascals triangel

order you do transformations in

1. horizontal shift

2. horizontal dilation f(x) = (1/3x)

3. vertical dilation

4. reflection

5. vertical shift

arc length formula

unit circle values

csc²x = (trig identity)

1 + cot²x

sec²x= (trig identity)

1 + tan²x

1= (trig identity)

sin²x + cos²x

sin(a+b)= trig identity

sin(a)cos(b) + cos(a)sin(b)

cos(a+b)= trig identity

cos(a)cos(b) - sin(a)sin(b)

sin(2x)= trig identity

2sin(x)cos(x)

cos(2x)= trig identity

• cos²(x) - sin²(x)

• 2cos²(x) - 1

• 1 - 2sin²(x)

VA of tan x=

π/2 +πn

VA of cot x=

πn

VA of sec x=

π/2 + πn

VA of csc x=

πn

polar to rectangular coordinate formula

x = r cos(θ), y = r sin(θ)

rectangular to polar coordinate formula

r =√(x² + y²), θ = tan^-1(y/x)

arithmetic sequence formula

a_n = a_k + d(n-k)

geometric sequence formula

g_n = g_k(R)^(n-k)

how does a exponential function look when a>0 and b>1

how does a exponential function look when a>0 and 0<b<1

if r = f(θ) is positive and increasing the distance from the origin is…

increasing

if r = f(θ) is negative and increasing the distance from the origin is…

decreasing

if r = f(θ) is negative and decreasing the distance from the origin is…

increasing