30 points, would be great if someone helped!

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.

Step-by-step explanation:

What we want to do is use the data to find the equation of the sinusoidal wave in order to plot it.

A sinusoidal wave is given by the formula

y  = A* sin(kx+o)

Where A is the amplitude of the sine (distance from x axis to the highest or lowest poin the graph reaches in the y-axis), k is the scale of the horizontal axis, and o is the phase.

Let's say the y-axis is for temperature in Celsius and the x-axis is time in minutes.

We are given that the highest temperature of the liquid is 18. Hence, the amplitude is 18.

A =18 ºC

Also we know the temperature is 12 ºC at the beginning, which means

y = 12 ºC when x = 0 min.

Substitute in the formula:

12  = 18*sin(0+o)

And solve for the phase o

o = arcsin(0.666) = 0.729 rad

Then we are given that y = 18 ºC after 2 minutes (x = 2 min). So substitute in the equation to find k

18 = 18*sin(k*(2)+0.729)

k*(2)+0.729 = arcsin(1) = π/2

k = 0.420

Now substitute A and the calculated values for k and o. This is the formula of the sinusoidal wave we must plot

y  = 18* sin(0.420x+0.729)

We can use the a free software to plot the formula. The final graph is attached.

The start and end of the two complete cycles are indicated by the yellow bar. One cycle is when, once the temperature is 12 degrees, it reaches 12 degrees again.

180

step-by-step explanation: