Question

Sketch two complete cycles of the sinusoidal function described in the scenario.

The temperature of a liquid varies sinusoidally as it is heated and then cooled repeatedly during an experiment. The temperature of the liquid is initially 12°C. The liquid is heated and reaches its first maximum temperature of 18°C after 2 minutes. The liquid is then placed in an ice bath and cooled to its minimum temperature.

Answer 1

Graph attached below

Explanation:

Since we don't know the units of the axis, i will assume the y axis represent temperature in celsius. Ant the x axis represent time in minutes.

The general term of a sine is the following

y = A* sin(kx+p)

Where A is the amplitude of the sine, k is the scale of the horizontal axis, and p is the phase.

A = 18 degrees, since it is the maximum temperature.

Now, at the initial time (x = 0), we are told y = 12 degrees

12 = 18* sin(0+p)

p = arcsin(0.666) = 0.7297 rad

And know we find k, (x = 2 minutes)

18 = 18*sin(k*(2)+0.7297)

k*(2)+0.7297 = arcsin(1) = pi/2

k = 0.4205

So the equation is

y = 18* sin(0.4205*x+0.7297)

We plot it using a graphing calculator