Key Features of Sinusoidal Functions

• Yes

• No

• Maybe

• What Graph?

Find the equation of the midline of the graph shown.

• y = 1

• y = 2

• y = 3

• y = 0

Find the amplitude of the graph shown.

• 2

• 4

• 6

• 8

Find the period of the graph shown.

• 2

• 4

• 6

• 8

The 4 key features that we'll use for sine/cosine graphs are

M: ​ (a)   ​

A: ​ (b)  

P: ​ (c)  

PS:​ (d)  

• midline

• amplitude

• period

• phase shift

y=Asin(B(x-C))+D is the standard form. A is the Amplitude B helps you find the period, B=2pi/period C is the phase shift D is the midline (vertical shift) For y=7sin(6(x-8))+9,

• 7

• amplitude

• 6

• midline

• 5

• phase shift

• 9

• helps calculate period

What is the amplitude of the function:
f(x) = ⅔sin(⅕θ) + 4

• ⅔

• ⅕

• ¾

• 4

• min: 13ºC

  max: 25ºC

• min: 17ºC

  max: 23ºC

• min: 5ºC

  max: 17ºC

• min: 8ºC

  max: 30ºC

The temperature in an office is controlled by an electronic thermostat. The temperatures vary according to the sinusoidal function: y = 5 sin( 90x ) +18 where y is the temperature (ºC) and x is the time in hours past midnight. What are the minimum and maximum temperatures in the office?

• 12ºC and 23ºC

• 13ºC and 23ºC

• 5ºC and 18ºC

• 11ºC and 23ºC

Sine or Cosine?

• y=sinx

• y=cosx