Alpha Trigonometry Topic Test FAMATState Convention 2011

The use of a calculator is not permitted!

For all questions, choice E is NOTA, meaning “none of these answers.”

All measurements are given in units, unless otherwise specified.

For inverse trigonometric functions, assume standard textbook domains and ranges.

Let

For questions #1-2, let

  1. Evaluate

A) / B) / C) / D) / E) NOTA
  1. Evaluate

A) / B) / C) / D) / E) NOTA

A) / B) / C) / D) / E) NOTA

A) / B) / C) / D) / E) NOTA
  1. What is the amplitude of

A) 2 / B) 7 / C) / D) / E) NOTA
  1. In triangle CAM, AM=6, CM=7, and CA=8. Evaluate

A) / B) / C) / D) / E) NOTA
  1. In what quadrant does the terminal side of the angle with measure 20102011°? And since I’m such a nice person, I will tell you that you will need to complete 55,838 rotations to find the terminal side.

A) Quadrant I / B) Quadrant II / C) Quadrant III / D) Quadrant IV / E) NOTA
  1. What is the domain of

A) / B)
C) / D)
E) NOTA
  1. Which of the following is equivalent to

A) / B)
C) / D)
E) NOTA
  1. Find the sum of the solutions to on the domain (Hint: Group Factor and use the zero-product property to find unit circle values that work.)

A) / B) / C) / D) / E) NOTA
  1. Evaluate

A) / B) / C) / D) / E) NOTA
  1. Evaluate , given that , , and

A) -2 / B) -1 / C) 0 / D) 2 / E) NOTA
  1. Given the following information, determine the proper sinusoidal function to match the data given.
  • The maximum value is 8
  • The minimum value is -2
  • The frequency is one-half.
  • The function has a negative phase shift (to the left of the origin) of units.

A) / B)
C) / D)
E) NOTA
  1. Trigonometric functions can be defined over the set of complex numbers. Evaluate over the set of complex numbers. Let (Hint: Be sure to draw a triangle! You should get an imaginary value for the length of the hypotenuse.)

A) / B) / C) / D) / E) NOTA
  1. Evaluate the cosine of the angle between the vectors and .

A) / B) / C) / D) / E) NOTA
  1. Hopefully by the time you get to this question, it will be 1:30 pm (if it is, then you are going at a great pace!) You stare at your wristwatch (which is analog, of course) and you notice that the length of the hour hand is 2 cm and the length of the minute hand is 4 cm. Now instead of finishing this test, you decide to determine the distance between the tip of the hour and minute hand at exactly 1:30:00 pm, which is…

A) / B) / C) / D) / E) NOTA
  1. Again, you are more enthused with your watch than your test (the same watch from the above problem), so you will tell me the length of the arc swept out by the hour hand from 1:00:00 pm up to 1:30:00 pm. Now after you finish this problem, stop looking at your watch and get back to this test!

A) / B) / C) / D) / E) NOTA
  1. (Hint: Use Euler’s Formula and a trig identity and recall that Sine is an ODD function and Cosine is an EVEN function…)

A) / B) / C) / D) / E) NOTA
  1. For defined values of (Hint: Check your identities!)

A) / B) / C) / D) / E) NOTA
  1. (Hint: Check your identities!)

A) / B) / C) / D) / E) NOTA
  1. Using the figure to the right, evaluate

A) / B)
C) / D) Not enough information
E) NOTA
  1. How many asymptotes does the function have?

A) 0 / B) 1 / C) 2 / D) 3 / E) NOTA

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