Exam 9: Trigonometric Identities and Their Applications

How many solutions does have for ?

Does ?

Using the sum or difference formulas, . Round both answers to 4 decimal places.

Write in the form .

Does

The following table gives, the percentage of the electorate favoring candidate A during the 12 months preceding a presidential election. Time, t, is measured in months, and t = 0 is a year before election day. Assume thatIs approximately trigonometric. A second candidate, candidate B, has a percentage of candidate support given by LetFor What is the meaning of the maximum of?

A ferris wheel sitting on the ground is 22 meters in diameter and makes one revolution every 5 minutes. If you start in the 9 o'clock position at t= 0 and the wheel is rotating clockwise, when is the first time that are you 16.5 meters above the ground?

Does ?

Find the exact value of .

Is the square of a complex number always real and nonnegative?

Either show the following equation is true, or find a value of x for which the equation is false:

Write in terms of the cotangent function.

The following table gives , the percentage of the electorate favoring candidate A during the 12 months preceding a presidential election. Time, t, is measured in months, and t = 0 is a year before election day. If were approximately trigonometric, its formula could be written . Round the second answer to 3 decimal places.

Two weights (weight 1 and weight 2) are suspended from the ceiling by springs. At time t = 0 (t in seconds), the weights are set in motion and begin bobbing up and down. Eventually, however, the oscillation of both weights dies down. The following equations describe the distance of each weight from the ceiling as a function of time: and . Which weight has oscillations which die down the fastest?

Two weights (weight 1 and weight 2) are suspended from the ceiling by springs. At time t = 0 (t in seconds), the weights are set in motion and begin bobbing up and down. Eventually, however, the oscillation of both weights dies down. The following equations describe the distance of each weight from the ceiling as a function of time: and . At what time are the two weights farthest apart?

The following table gives , the percentage of the electorate favoring candidate A during the 12 months preceding a presidential election. Time, t, is measured in months, and t = 0 is a year before election day. Assume that is approximately trigonometric. A second candidate, candidate B, has a percentage of support given by . What is the largest value of t, , at which the two candidates are tied for electoral support? Round to 2 decimal places.

How many solutions does have for ?

Find the smallest value of t such that and .

A mass attached to a spring moves horizontally on a frictionless track. Its displacement from the rest position at time t is given by . What is the furthest distance from the rest position that the mass will achieve? The displacement is measured in meters.