Key Features of Sinusoidal Functions

Examine the equation  $$y=-\cos\left(x-\frac{\pi}{4}\right)+2$$  and the graph above. Does the graph represent the equation?

Find the equation of the midline of the graph shown.

Find the amplitude of the graph shown.

Find the period of the graph shown.

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

M: ​ (a)   ​

A: ​ (b)  

P: ​ (c)  

PS:​ (d)  

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,

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

The temperature in an office is controlled by an electronic thermostat. The temperatures vary according to the sinusoidal function:
$$y=19+6\sin\left(\frac{π}{12}(x–11)\right)$$
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?

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?

Sine or Cosine?