Contents
- Preface
7The Unit Circle: Sine and Cosine Functions
9Trigonometric Identities and Equations
- Introduction to Trigonometric Identities and Equations
- 9.1Verifying Trigonometric Identities and Using Trigonometric Identities to Simplify Trigonometric Expressions
- 9.2Sum and Difference Identities
- 9.3Double-Angle, Half-Angle, and Reduction Formulas
- 9.4Sum-to-Product and Product-to-Sum Formulas
- 9.5Solving Trigonometric Equations
11Systems of Equations and Inequalities
- AProofs, Identities, and Toolkit Functions
- Index
Key Terms
Key Terms
- absolute maximum
- the greatest value of a function over an interval
- absolute minimum
- the lowest value of a function over an interval
- average rate of change
- the difference in the output values of a function found for two values of the input divided by the difference between the inputs
- composite function
- the new function formed by function composition, when the output of one function is used as the input of another
- decreasing function
- a function is decreasing in some open interval if for any two input values and in the given interval where
- dependent variable
- an output variable
- domain
- the set of all possible input values for a relation
- even function
- a function whose graph is unchanged by horizontal reflection, and is symmetric about the axis
- function
- a relation in which each input value yields a unique output value
- horizontal compression
- a transformation that compresses a function’s graph horizontally, by multiplying the input by a constant
- horizontal line test
- a method of testing whether a function is one-to-one by determining whether any horizontal line intersects the graph more than once
- horizontal reflection
- a transformation that reflects a function’s graph across the y-axis by multiplying the input by
- horizontal shift
- a transformation that shifts a function’s graph left or right by adding a positive or negative constant to the input
- horizontal stretch
- a transformation that stretches a function’s graph horizontally by multiplying the input by a constant
- increasing function
- a function is increasing in some open interval if for any two input values and in the given interval where
- independent variable
- an input variable
- input
- each object or value in a domain that relates to another object or value by a relationship known as a function
- interval notation
- a method of describing a set that includes all numbers between a lower limit and an upper limit; the lower and upper values are listed between brackets or parentheses, a square bracket indicating inclusion in the set, and a parenthesis indicating exclusion
- inverse function
- for any one-to-one function the inverse is a function such that for all in the domain of this also implies that for all in the domain of
- local extrema
- collectively, all of a function's local maxima and minima
- local maximum
- a value of the input where a function changes from increasing to decreasing as the input value increases.
- local minimum
- a value of the input where a function changes from decreasing to increasing as the input value increases.
- odd function
- a function whose graph is unchanged by combined horizontal and vertical reflection, and is symmetric about the origin
- one-to-one function
- a function for which each value of the output is associated with a unique input value
- output
- each object or value in the range that is produced when an input value is entered into a function
- piecewise function
- a function in which more than one formula is used to define the output
- range
- the set of output values that result from the input values in a relation
- rate of change
- the change of an output quantity relative to the change of the input quantity
- relation
- a set of ordered pairs
- set-builder notation
- a method of describing a set by a rule that all of its members obey; it takes the form
- vertical compression
- a function transformation that compresses the function’s graph vertically by multiplying the output by a constant
- vertical line test
- a method of testing whether a graph represents a function by determining whether a vertical line intersects the graph no more than once
- vertical reflection
- a transformation that reflects a function’s graph across the x-axis by multiplying the output by
- vertical shift
- a transformation that shifts a function’s graph up or down by adding a positive or negative constant to the output
- vertical stretch
- a transformation that stretches a function’s graph vertically by multiplying the output by a constant