History
Period of Sinusoidal Functions
Axis of the curve of Sinusoidal Functions
Solving the Equations of Sinusoidal Functions
Amplitude of Sinusoidal Functions
100

What does the Greek word Trigono mean?

Triangle

100

What is a period

The length of one cycle

100

What variable represents the axis of the curve in the following equation: y=a sin k(x-d)+c.

The variable "c" represents the axis of the curve.
100

What is sinø = 1, where 0o ≤ ø ≥ 360o

ø = 90o

100

What variable represents the amplitude in the following equation: y=a sin k(x-d)+c.

The variable "a" represents the amplitude.

200

What does the word Trigonometry mean, literally? (two words)

Triangle Measurement

200

What affects the period given the equation?

y = a sin k (x - d) + c

k

200

Name all the transformations that affect the axis of the curve of a sinusoidal function.

Vertical translation and a reflection over the x-axis after all transformations are completed.

200

What is sinø = 1/2, where 0 ≤ ø ≥ ℼ/2

ø = ℼ/6

200

Name all the transformations that affect the amplitude of a sinusoidal function.

Vertical expansion or compression.

300

When was the earliest known example of the use of trigonometry?

3000 BCE

300

How do you calculate the period of a function in terms of pi? (formula)

P = 2ℼ/|k|

300

Define the axis of the curve.

Midpoint/Average of the function

300

Can the maximum value of a sine wave be greater than one if no transformations are done to it?

No.

300

Define amplitude.

The vertical distance from the axis of the curve to either the maximum or minimum value is called the amplitude of the function.

400

Which Persian mathematician, also known as the father of algebra, discovered the tan ratio?

Al-Kwarizmi

400

What is an attribute of period that was mentioned in the presentation?

It is self-replicating

400

What is the equation you use in order to find the axis of the curve?

Max+Min/2=Axis of the Curve

400

Solve, sin(ø - 1) = √3/2, where 0 ≤ ø ≥ 2ℼ (to 3 significant digits)

ø = 2.047, 3.094

400

What is the equation you use in order to find the amplitude?

Max-Min/2=Amplitude

500

What was the name of the Indian Astronomer that found the value of pi to 4 digits?

Aryabhata

500

What is the period of y=cos4ø in terms of pi?

P = ℼ/2

500

Solve, sin4ø = 0.5, where 0 ≤ ø ≥ 2ℼ (find all possible solutions)

ø = ℼ/24, 5ℼ/24, 13ℼ/24, 17ℼ/24, 25ℼ/24, 29ℼ/24, 37ℼ/24, 41ℼ/24

500

Where does the word amplitude originate from and what does it mean?

Originated from the Latin word amplus which means large/spacious

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