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Math 142 - Midterm 1 Practice
1. Consider the function
f (x) = csc(π(x − 1)) + 2.
(a) What is the domain of f (x)?
(b) What is the range of f (x)?
(c) What is the period of f (x)?
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2. A 3 cm diameter pully and 5 cm diameter pully are fixed to the same axel, and a drive belt is
attached to each pully. The belt attached to the 5 cm pully is driven at a speed of 20 cm/s.
How far does the other belt move in 15 seconds?
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3. The population of a tourist town varies throughout the year, with the peak population in the
summer. The town’s tourism board has the following data:
day
59
150
241
332
423
population
97795
102000
74241
46002
73518
(a) Find a sinusoidal function that models this data.
(b) What population does your model give for day 241? Are you satisfied with how well
your model fits the data?
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4. Solve the following equations. Be sure to find every solution, if there are multiple solutions.
(a) tan−1 u = 0.334
(b) 3 sin(x3 + 1) = 2
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5. Verify the following trigonometric identities.
(a) sec θ − cos θ = sin θ tan θ
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(b) sec u − tan u =
cos u
1 + sin u