MHF 4U Final Exam Review
Chapter 3: Trigonometric Functions
Knowledge/Understanding:
3K1. Convert from radians to degrees.
a) b) c) d) e)
3K2. Convert from degrees to radians.
a) 120° b) 30° c) 270° d) 330° e) 135°
3K3. Use the CAST rule to state the sign of each value. Check using a calculator.
a) b) sin120o c) d) tan(-15)o e) f) sin(-45)o
3K4. Evaluate the following using special triangles
a) b) c) d) e) f)
3K5. State the amplitude, period, phase shift, and vertical translation for each function.
a)
b)
c)
Application:
3A1. Mr. McMillan has an ant farm. He decides to have a carnival for his ants. An ant boards the mini Ferris wheel which has a radius of 25cm and its center is 26cm above the ground. It rotates once every 50 seconds. Suppose the ant gets on this fun carnival ride at the bottom at t=0.
a) Write an equation for the function.
b) Use your equation to determine how high the ant will be above the ground after:
i) 10 seconds ii) 20 seconds iii) 40 seconds
3A2. The average monthly temperature of Windsor can be modeled by , where T is the temperature in degrees Celsius and represents January 1, represents February 1, and so on.
a) When is the average monthly temperature highest? Lowest?
b) Use the model to predict when the temperature is 0oC.
c) When does the temperature reach 25oC?
3A3. The vertical distance, in metres, of a rider with respect to the horizontal diameter of a Ferris wheel is modeled by , where t is the number of seconds elapsed.
a) When is the rider first at 4.5m? –3.2m?
b) When is the third time the rider is at –25m?
3A4. The table shows the average number of popsicles bought each month in Arkansas.
Month / J / F / M / A / M / J / J / A / S / O / N / DAverage popsicles sold / 95.5 / 112.6 / 150.5 / 187.7 / 229.7 / 254.9 / 278 / 244 / 184.7 / 145.7 / 82.3 / 72.6
a) Create a scatter plot of the number of popsicles sold versus time, where t=1 represents January, t=2 represents February, and so on.
b) Draw the curve of best fit.
c) Determine the trigonometric function that models this relation.
d) When will the number of monthly amount of popsicles sold be at a maximum according to the function? When will it be a minimum according to the function?
e) How good a model is the equation? Explain.
3A5. Graph the function
3A6. Graph the function , for -2p £ q £ 2p.
Communication:
3C1. What is a radian?
3C2. The equation of the temperature in Thunder Bay is . Explain what each of the variables (x and y) and constants (a, k, c, d) represent.
TIPS:
3T1. The diameter of a car’s tire is 50cm. While the car is being driven, the tire picks up a nail.
a) Model the height of the nail above the ground in terms of the distance the car has traveled since the tire picked up the nail.
b) How high above the ground will the nail be after the car has traveled 0.5km?
c) The nail reaches a height of 10cm above the ground for the sixth time. How far has the car traveled?
d) What assumption must you make concerning the driver’s habits for the function to give an accurate height?
Chapter 3 Answers:
Knowledge/Understanding Answers:
3K1. a) 120° b) 240° c) 180° d) 45° e) 150°
3K2. a) b) c) d) e)
3K3. a) + b) + c) - d) - e) - f) -
3K4. a) b) c) d) e) 1 f)
3K5. a)
b)
c)
Application Answers:
3A1. a)
b) i) 18cm ii) 46cm iii) 18cm
3A2. a) maximum: July, minimum: January
b) December and January
c) May and August
3A3. a) 1.4s,7.2s
b) 26.7s
3A4. c) H(t)= -102.7cost + 175.3
d) maximum: June, minimum: December
e) The model is reasonable but not exact. Individual results vary up to 10%.
3A5. 3A6.
Communication Answers:
3C1. A radian is a measure of an angle subtended by an arc that is equal length to the radius.
3C2. x: month number, y: temperature at month number x in degrees Celsius, a: the amount the maximum temperature is above the average and the amount the minimum temperature is below the average, k: related to the time it takes for one cycle (i.e. one year), c: represents when the temperature is at an average value and increasing, d: average temperature
TIPS Answers:
3T1. a)
b) 34.19cm
c) 450m
d) The driver moves in a continuous way meaning no spinning of the tires or skidding to a stop.