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Real-World Applications of Trigonometric Functions, Page 8

Ferris Wheel Example (continued)

To find out when the Ferris wheel reaches a height of 55 meters, solve the equation for t when y = 55.

55 = 30.75 sin(2pi/4.5 t) + 34.75; 20.25 = 30.75 sin(2pi/4.5 t); 20.25/30.75 = sin(2pi/4.5 t); sine inverse of (20.25/30.75) = 2pi/4.5 t

Remember to make sure your calculator is set on radian mode.

.719 = 2pi/4.5 t; t = .719(4.5)/2pi; t is approximately .515

Sarah will reach a height of 55 meters 0.515 minutes after she starts her ride.

Convert the minutes into seconds:

.515 mintues x 60 seconds over 1 minute equals 30.9seconds

If Sarah starts her ride at 12:30 pm, then she will reach a height of 55 meters at approximately 12:30.31 pm.