Exam 9: Trigonometric Identities and Their Applications

What is the smallest positive solution to ? Round to 2 decimal places.

Does ?

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 is closer to the ceiling at time t = 2?

What is for ?

What is the smallest positive solution to ? Round to 2 decimal places.

What is the smallest positive solution to ? Round your answer to 2 decimal places.

Does ?

How many solutions does have for ?

Write in terms of the tangent function.

A ferris wheel sitting on the ground is 24 meters in diameter and makes one revolution every 7 minutes. If you start in the 9 o'clock position t= 0 and the wheel is rotating clockwise, write a formula for your height above the ground at time t.

Find the exact value of .

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

A ferris wheel sitting on the ground is 24 meters in diameter and makes one revolution every 7 minutes. If you start in the 9 o'clock position at t= 0 and the wheel is rotating counterclockwise, when is the first time that are you 6 meters above the ground?

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

Write in terms of the tangent function.

How many solutions does have for ? A)4 B)0 C)1 D) none of the above.

Write In the form .

The population in a town oscillates over a 15 year period beginning with a high of 3000 people in year and a low of 2300. Find a formula for the town's population.

If ,can also be written in the form ?

Find the smallest value of t such that and