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Exam 9: Trigonometric Identities and Their Applications

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Question 21

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A mass attached to a spring moves horizontally on a frictionless track. Its velocity at time t is given by . What is the maximum velocity that the mass will achieve? The displacement is measured in meters and the time is measured in seconds.

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Question 22

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If can also be written in the form .

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Question 23

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Does ?

Write in the form .

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

Write in the form .

The deer population in a state park is modelled by where t is the number of months since January 1, 2005. Evaluate and interpret the result. Round to the nearest whole number.

The deer population in a state park is modelled by where t is the number of months since January 1, 2005. If , find the value(s) of t at which the deer population is equal to 280. Round your answer to the nearest tenth.

Which of the following statements are identities?

Find the smallest value of t such that and .

The population in a town oscillates over a 7 year period beginning with a high of 3000 people in year t= 0 and a low of 2300. Find a formula for the town's population.

Calculate exactly.

Find the smallest value of t such that and .

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

A ferris wheel sitting on the ground is 20 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 counterclockwise, write a formula for your height above the ground at time t.

Find a formula for a deer population which oscillates over a 6 year period between a low of 1000 in year t=0 and a high of 2900 in year t=3 .

Does ?

A mass attached to a spring moves horizontally on a frictionless track. Its displacement from the rest position at time t is given by . If displacement is measured in inches and time is measured in inches, when is the mass 0.3 inches from the rest position? Restrict your answer(s) to , and round to 3 decimal places.

A ferris wheel sitting on the ground is 26 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 counterclockwise, write a formula for your height above the ground at time t.