Trigonometry

Question 1

General Equation for a Sine Wave

Answer 1

A = amplitude

f = ordinary frequency (cycles/time)

w = angular frequency (radians/second)

phi = phase (radians at t = 0)

Question 2

Unit Circle

Answer 2

Question 3

Tangent and Cotangent Identities

Answer 3

Question 4

Reciprocal Identities

Answer 4

Question 5

Pythagorean Identities

Answer 5

Question 6

Even/Odd Formulas

Answer 6

Question 7

Periodic Formulas

Answer 7

Question 8

Double Angle Formulas

Answer 8

Question 9

Half Angle Formulas (Standard Format)

Answer 9

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

Question 10

Half Angle Formulas (Alternate Format)

Answer 10

Question 11

Sum and Difference Formulas

Answer 11

Question 12

Product to Sum Formulas

Answer 12

Question 13

Sum to Product Formulas

Answer 13

Question 14

Cofunction Formulas

Answer 14

Question 15

Inverse Definitions

Answer 15

Question 16

Inverse Properties

Answer 16

Question 17

Law of Sines

Answer 17

Question 18

Law of Cosines

Answer 18

Question 19

Law of Tangents

Answer 19

Question 20

Euler’s Formula

Answer 20

e^iπ + 1 = 0

Question 21

Sin / Cos Graphs

Answer 21

Question 22

Tan / Cot Graphs

Answer 22

Question 23

Sec / Csc Graphs

Answer 23

Question 24

Range vs. Domain

Answer 24

Domain is input

Range is output

Question 25

What is the fundamental property of an inverse function

Answer 25

There is one and only one output for every input

to derive it, swap f(x) and x and solve

Question 26

Clues that a function does not have an inverse

Answer 26

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

Question 27

Quick inverse functions

Answer 27

inverse of e^x is ln(x)

inverse of log_ax is a^x

inverxe of sin(x) is sin^-1(x)

Question 28

How to shift a function up, down, or sideways

Answer 28

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)

Question 29

How to reflect a function up and down or left and right

Answer 29

reflect up and down (outputs changed): -f(x)

reflect left and right (inputs changed): f(-x)

Question 30

What is the approximate measure of a radian

Answer 30

about 57 degrees (about 6 per circle)

Question 31

GCF / Difference of Squares / Sum or Difference of Cubes

(Factoring Binomials)

Answer 31

Question 32

How to make the tangent graph wider

How to make the tangent graph less intense at the inflection point

Answer 32

divide theta by a constant

multiply the tangent function by a constant

Question 33

Best way to draw the SEC / CSC graphs

Answer 33

Draw the SIN / COS graph, then above it, plot the inverse