Trig Help

Solutions are at the end of the quiz.

  1. Convert 135° to radians.
  2. Name an angle that is equivalent to π/3 radians.
  3. What is the reference angle of an angle with measure 7π/6 radians?
  4. In right triangle trigonometry, how is the cotangent function defined?
  5. In what quadrants is the cosecant function negative?
  6. What are the values of  cos 5π/3  and sec 5π/3?
  7. Complete the trig identity:   sin 2θ =  _________________ .
  8. Solve the equation 2 sin2 θ - sin θ – 1 = 0  for θ.  Your answer should consist of angles satisfying  0 ≤ θ < 2π.
  9. At what angles is the tangent function undefined?
  10. What is the graph of y=sin ?   What is the graph of y-2sin ?
  11. What is the domain and range of the inverse sine function?
  12. What is the value of cos-1 ?

We’re handing this out to you to help you assess your “trig readiness.” You’re encouraged to work on these questions to see how you do (answers are below), but it’s also OK to look them over and just see how familiar they are.

How should you rate yourself? Here are some reactions you can have that probably indicate that you’re in good shape:

  • I remember doing all but one or two of these in precalculus.
  • I could answer about half of these questions immediately (or once my brain recovers from summer).
  • With time to work, I could figure out the answers to about ¾ of these questions.

Here are some reactions that indicate you probably need to work on your trig skills, and perhaps take the trigonometry refresher being offered this semester:

  • I have never had to learn the values of trig functions at standard angles on the unit circle.
  • I have never seen about half of these questions.

We will be happy to help you determine if you should consider sitting in on the trig refresher. There will be some trig review in Calculus I, but you are expected to have some prior experience with trig, or be able to pick up a number of things on your own or in the trig course. Let us know how we can help.

 

Solutions

Answers to Trigonometry Questions You Should Be Able To Answer (Without Using a Calculator)

  1. 3π/4.
  2. Two possible answers are  -5π/3 and 7π/3.
  3. π/6.
  4. cotangent = adj_opp.
  5. The third and fourth quadrants.
  6. cos 5π/3 =  1/2;  sec 5π/3 = 2.
  7. 2 sin θ  cos θ.
  8. θ = π/2,  θ = 7π/6;  θ = 11π/6.
  9. At angles of the form  θ = k π/2,  where k is an odd integer (those are the angles at which the cosine function has value zero).
  10. Graph of   y=sin :

    graph1

  11. Graph of  y-2sin :

    graph2

  12. domain [-1,1], range -π/2  ≤  θ  ≤  π/2.
  13. π/6.

 

 

Created by Mathematica (August 25, 2006)



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