Trigonometry Flashcards

1
Q

General Equation for a Sine Wave

A

A = amplitude

f = ordinary frequency (cycles/time)

w = angular frequency (radians/second)

phi = phase (radians at t = 0)

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2
Q

Unit Circle

A
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3
Q

Tangent and Cotangent Identities

A
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4
Q

Reciprocal Identities

A
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5
Q

Pythagorean Identities

A
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6
Q

Even/Odd Formulas

A
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7
Q

Periodic Formulas

A
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8
Q

Double Angle Formulas

A
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9
Q

Half Angle Formulas (Standard Format)

A

Also: Tan(theta/2) = (1-cos(theta))/sin(theta)

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10
Q

Half Angle Formulas (Alternate Format)

A
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11
Q

Sum and Difference Formulas

A
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12
Q

Product to Sum Formulas

A
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13
Q

Sum to Product Formulas

A
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14
Q

Cofunction Formulas

A
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15
Q

Inverse Definitions

A
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16
Q

Inverse Properties

17
Q

Law of Sines

18
Q

Law of Cosines

19
Q

Law of Tangents

20
Q

Euler’s Formula

A

e + 1 = 0

21
Q

Sin / Cos Graphs

22
Q

Tan / Cot Graphs

23
Q

Sec / Csc Graphs

24
Q

Range vs. Domain

A

Domain is input

Range is output

25
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
26
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
27
Quick inverse functions
inverse of ex is ln(x) inverse of logax is ax inverxe of sin(x) is sin-1(x)
28
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)
29
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)
30
What is the approximate measure of a radian
about 57 degrees (about 6 per circle)
31
GCF / Difference of Squares / Sum or Difference of Cubes (Factoring Binomials)
32
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
33
Best way to draw the SEC / CSC graphs
Draw the SIN / COS graph, then above it, plot the inverse
34