Modelling with Trigonometrical Functions

History

100

What does the Greek word Trigono mean?

Triangle

200

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

Triangle Measurement

300

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

3000 BCE

400

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

Al-Kwarizmi

500

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

Aryabhata

Period of Sinusoidal Functions

100

What is a period

The length of one cycle

200

What affects the period given the equation?

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

k

300

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

P = 2ℼ/|k|

400

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

It is self-replicating

500

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

P = ℼ/2

Axis of the curve of Sinusoidal Functions

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.

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.

300

Define the axis of the curve.

Midpoint/Average of the function

400

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

Max+Min/2=Axis of the Curve

Solving the Equations of Sinusoidal Functions

100

What is sinø = 1, where 0^o ≤ ø ≥ 360^o

ø = 90^o

200

What is sinø = 1/2, where 0 ≤ ø ≥ ℼ/2

ø = ℼ/6

300

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

No.

400

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

ø = 2.047, 3.094

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

Amplitude of Sinusoidal Functions

100

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

The variable "a" represents the amplitude.

200

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

Vertical expansion or compression.

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

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

Max-Min/2=Amplitude

500

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

Originated from the Latin word amplus which means large/spacious