Unit 3.4 - 3.7 Review

A race car fan is standing in one spot cheering . The race car is 10 feet away from fan when it is in the starting line and 50 feet from them when on the opposite side from the fan. The race car takes 60 seconds to make a complete rotation. At time 𝑡 = 0, the race car is in the starting line, (0, 10). The sinusoidal function 𝑓 models the distance between the race car and the fan, in feet, as a function of time, in seconds.

1. The function 𝑓 can be written in the form of 𝑓(𝑡) = 𝑎 sin(𝑏(𝑡 + 𝑐)) + 𝑑.

2. Find the values of the constants 𝑎.

A race car fan is standing in one spot cheering . The race car is 10 feet away from fan when it is in the starting line and 50 feet from them when on the opposite side from the fan. The race car takes 60 seconds to make a complete rotation. At time 𝑡 = 0, the race car is in the starting line, (0, 10). The sinusoidal function 𝑓 models the distance between the race car and the fan, in feet, as a function of time, in seconds.

1. The function 𝑓 can be written in the form of 𝑓(𝑡) = 𝑎 sin(𝑏(𝑡 + 𝑐)) + 𝑑.

2. Find the values of the constants b.

A race car fan is standing in one spot cheering . The race car is 10 feet away from fan when it is in the starting line and 50 feet from them when on the opposite side from the fan. The race car takes 60 seconds to make a complete rotation. At time 𝑡 = 0, the race car is in the starting line, (0, 10). The sinusoidal function 𝑓 models the distance between the race car and the fan, in feet, as a function of time, in seconds.

1. The function 𝑓 can be written in the form of 𝑓(𝑡) = 𝑎 sin(𝑏(𝑡 + 𝑐)) + 𝑑.

2. Find the values of the constants d.

A race car fan is standing in one spot cheering . The race car is 10 feet away from fan when it is in the starting line and 50 feet from them when on the opposite side from the fan. The race car takes 60 seconds to make a complete rotation. At time 𝑡 = 0, the race car is in the starting line, (0, 10). The sinusoidal function 𝑓 models the distance between the race car and the fan, in feet, as a function of time, in seconds.

1. The function 𝑓 can be written in the form of 𝑓(𝑡) = 𝑎 sin(𝑏(𝑡 + 𝑐)) + 𝑑.

2. Find the values of the constants c.

A race car fan is standing in one spot cheering . The race car is 10 feet away from fan when it is in the starting line and 50 feet from them when on the opposite side from the fan. The race car takes 60 seconds to make a complete rotation. At time 𝑡 = 0, the race car is in the starting line, (0, 10). The sinusoidal function 𝑓 models the distance between the race car and the fan, in feet, as a function of time, in seconds.

1. The graph of 𝑓 and its dashed midline for two full cycles is shown.

2. Determine the possible coordinate (𝑡, 𝑓(𝑡)) for the point R

Answer explanation

Race car takes 60 seconds to complete 1 full rotation, meaning the period is 60 seconds.

Recall min to min or max to max is the period. Look at the graph, we start at the min (0,10) and R is the second min. Therefore, R is (60,10)

A race car fan is standing in one spot cheering . The race car is 10 feet away from fan when it is in the starting line and 50 feet from them when on the opposite side from the fan. The race car takes 60 seconds to make a complete rotation. At time 𝑡 = 0, the race car is in the starting line, (0, 10). The sinusoidal function 𝑓 models the distance between the race car and the fan, in feet, as a function of time, in seconds.

1. The graph of 𝑓 and its dashed midline for two full cycles is shown.

2. Determine the possible coordinate (𝑡, 𝑓(𝑡)) for the point Q.

Answer explanation

A race car fan is standing in one spot cheering . The race car is 10 feet away from fan when it is in the starting line and 50 feet from them when on the opposite side from the fan. The race car takes 60 seconds to make a complete rotation. At time 𝑡 = 0, the race car is in the starting line, (0, 10). The sinusoidal function 𝑓 models the distance between the race car and the fan, in feet, as a function of time, in seconds.

1. The graph of 𝑓 and its dashed midline for two full cycles is shown.

2. Determine the possible coordinate (𝑡, 𝑓(𝑡)) for the point P

Answer explanation