1' Determine the coordinates of the trigonometric point:

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MTH-5108 Pretest B
1. Determine the coordinates of the
trigonometric point
2. Calculate the angle in radians from the
interval where t ? -4p,-2p and corresponding to
the following ordered pair.
3. What is the image for the following
trigonometric function, if f(t) cot t
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• Given the following functions f(x) sin x, g(x)
  cos x and h(x) tan x
• a) Within the interval -p,p, determine where
  each of the 3 functions are positive?
• b) Within the interval -p,p, determine where
  each of the 3 functions are increasing?
• c) What are the values of x when function h(x)
  is a minimum when x ? ??

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• Simplify the following

• Prove the following identity

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• What is the phase shift?
• What is the period?
• What is the range?
• What are the zeros?

• Find the equation of the sinusoidal function
  shown below where a is positive.

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• Which of the following graphs is a transformation
  of f(x) cos x where
• Amplitude is 2
• Vertical translation of 1
• Period is 2p

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• The position of a piston as a function of time
  can be represented by the following sinusoidal
  function
• where t is time in seconds.
• If the movement of this piston is changed so that
  the period is doubled and the phase change
  remains the same,
• a) What will the new equation be?
• b) How many cycles will occur in 1 minute?
• c) What will be the position of the piston (to
  the nearest tenth) after 10 seconds?

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• Oceanographers collected data on the mass of
  whales over a 2-year period and observed that the
  mass of the whales varied according to the
  following function
• where m is the mass of the whales in tonnes and
  t is the number of months from the beginning of
  observation.
• a) During the two year period when was the
  whales mass at a maximum and at a minimum?
• b) After 12 months of observation, was their
  mass increasing or decreasing?
• c) At what point in time (to the nearest
  hundredth) was the whales mass 100 tonnes?