Trigonometry Flashcards
General Equation for a Sine Wave
A = amplitude
f = ordinary frequency (cycles/time)
w = angular frequency (radians/second)
phi = phase (radians at t = 0)
Unit Circle
Tangent and Cotangent Identities
Reciprocal Identities
Pythagorean Identities
Even/Odd Formulas
Periodic Formulas
Double Angle Formulas
Half Angle Formulas (Standard Format)
Also: Tan(theta/2) = (1-cos(theta))/sin(theta)
Half Angle Formulas (Alternate Format)
Sum and Difference Formulas
Product to Sum Formulas
Sum to Product Formulas
Cofunction Formulas
Inverse Definitions
Inverse Properties
Law of Sines
Law of Cosines
Law of Tangents
Euler’s Formula
eiπ + 1 = 0
Sin / Cos Graphs
Tan / Cot Graphs
Sec / Csc Graphs
Range vs. Domain
Domain is input
Range is output
What is the fundamental property of an inverse function
There is one and only one output for every input
to derive it, swap f(x) and x and solve
Clues that a function does not have an inverse
Even exponent, absolute value symbol, graph of function is a horizontal line, and if you draw a horizontal line through the graph of the function, and it hit’s the graph more than once
Quick inverse functions
inverse of ex is ln(x)
inverse of logax is ax
inverxe of sin(x) is sin-1(x)
How to shift a function up, down, or sideways
add a constant to the output to go up f(x)+C
subtract a constant from the output to go down f(x)-C
add a constant to the input to shift left f(x+C)
subtract a constant from the input to shift right f(x-C)
How to reflect a function up and down or left and right
reflect up and down (outputs changed): -f(x)
reflect left and right (inputs changed): f(-x)
What is the approximate measure of a radian
about 57 degrees (about 6 per circle)
GCF / Difference of Squares / Sum or Difference of Cubes
(Factoring Binomials)
How to make the tangent graph wider
How to make the tangent graph less intense at the inflection point
divide theta by a constant
multiply the tangent function by a constant
Best way to draw the SEC / CSC graphs
Draw the SIN / COS graph, then above it, plot the inverse
