Modeling Temperature with Trigonometric Functions

The video tutorial explains how to model daily temperature variations in Johannesburg using trigonometric functions. It starts by discussing the typical temperature range and then introduces a trigonometric function to represent these changes. The tutorial covers defining the function, calculating its amplitude and period, and adjusting it to model temperature from midnight. The process involves graphing and understanding the function's behavior over a 24-hour period.

What is the daily low temperature in Johannesburg in June?

• 3 degrees Celsius

• 10 degrees Celsius

• 10.5 degrees Celsius

• 18 degrees Celsius

At what times is the temperature typically at the midpoint between the daily high and low?

• 6:00 a.m. and 6:00 p.m.

• 12:00 p.m. and 12:00 a.m.

• 10:00 a.m. and 10:00 p.m.

• 4:00 p.m. and 4:00 a.m.

What is the highest temperature in Johannesburg in June?

• 10 degrees Celsius

• 10.5 degrees Celsius

• 18 degrees Celsius

• 3 degrees Celsius

What trigonometric function is suggested to model the temperature?

• Sine

• Cosine

• Cotangent

• Tangent

How is the midline of the trigonometric function determined?

• Average of the high and low temperatures

• Difference between the high and low temperatures

• Sum of the high and low temperatures

• Twice the low temperature

What is the amplitude of the temperature model?

• 3 degrees Celsius

• 18 degrees Celsius

• 10.5 degrees Celsius

• 7.5 degrees Celsius

What is the period of the trigonometric function used in the model?

• 12 hours

• 24 hours

• 18 hours

• 6 hours

At what time does the temperature reach its highest point according to the model?

• 4:00 p.m.

• 10:00 p.m.

• 10:00 a.m.

• 12:00 p.m.

What adjustment is made to model temperature T hours after midnight?

• Shift the graph to the right by 10 hours

• Shift the graph to the left by 10 hours

• Increase the amplitude by 10.5 degrees

• Decrease the period by 10 hours

What is the mathematical expression for the temperature model T hours after 10 a.m.?

• 7.5 * sin(pi/12 * T) + 10.5

• 7.5 * cos(pi/12 * T) + 10.5

• 7.5 * sin(2pi/24 * T) + 10.5

• 7.5 * cos(2pi/24 * T) + 10.5