terMInology | 115

● (^) Sinusoidal Function A periodic function is sinusoidal if it can be written in the form
fx()=-Axsin(()w hk) + for real numbers A, ω, h, and k. In this form,
○ (^) A is called the amplitude of the function,
○ (^2) wp is the period of the function,
○ 2 wp is the frequency of the function,
○ (^) h is called the phase shift, and
○ (^) the graph of yk= is called the midline.
Furthermore, we can see that the graph of the sinusoidal function f is obtained by first
vertically scaling the graph of the sine function by A, then horizontally scaling the
resulting graph by w^1 , and, finally, by horizontally and vertically translating the resulting
graph by h and k units, respectively.
● (^) Tangent Let θ be any real number such that q¹+p 2 kp for all integers k. In the Cartesian
plane, rotate the initial ray by θ radians about the origin.
Intersect the resulting terminal ray with the unit circle to get a point (xθ, yθ). The value of
tan(θ) is yxqq.
● (^) Trigonometric Identity A trigonometric identity is a statement that two trigonometric
functions are equivalent.
Module 3
● (^) e Euler’s number, e, is an irrational number that is approximately equal to
2.7182818284590.
● (^) Σ The Greek letter sigma, Σ, is used to represent the sum. There is no rigid way to
use Σ to represent a summation, but all notations generally follow the same rules.
The most common way it is used is discussed. Given the sequence a 1 , a 2 , a 3 , a 4 ,.. ., we can
write the sum of the first n terms of the sequence using the expression:
k
n
ak

å
1

.

● (^) Arithmetic Series An arithmetic series is a series whose terms form an arithmetic
sequence.
● (^) geometric Series A geometric series is a series whose terms form a geometric sequence.
● (^) Invertible Function Let f be a function whose domain is the set X and whose image is the
set Y. Then f is invertible if there exists a function g with domain Y and image X such that
f and g satisfy the property:
For all xXÎ and yYÎ , fx()=y if and only if gy()=x.
The function g is called the inverse of f and is denoted f-^1.
The way to interpret the property is to look at all pairs ()xy, Î ́XY: If the pair (x, y) makes
fx()=y a true equation, then gy()=x is a true equation. If it makes fx()=y a false
equation, then gy()=x is false. If that happens for each pair in XY ́ , then f and g are
invertible and are inverses of each other.