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Study Guide for Exam 4
This will be a closed-book exam. No calculators are permitted on this exam.
To do well on the exam, you should be able to do the following:
Section 5.1: The Unit Circle
- State the equation for the unit circle, and relate the equation to the distance formula we learned in Chapter 1.
- Define the terminal point (x,y) for a given real number t.
- State the terminal points for t=k⋅π6, t=k⋅π4, t=k⋅π3, and t=k⋅π2 where k is a given integer.
- Determine the reference number ˉt for a given real number t.
- Use the procedure in the grey box on page 406 of Stewart, Redlin, and Watson to find the terminal point for any real number t using t’s reference number ˉt.
Section 5.2: Trigonometric Functions of Real Numbers
- Relate the trigonometric functions sine (sin), cosine (cos), tangent (tan), secant (sec), cosecant (csc), and cotangent (cot) to the terminal point associated with a real number t.
- Evaluate the trigonmetric functions above at t=k⋅π6, t=k⋅π4, t=k⋅π3, and t=k⋅π2 where k is a given integer.
- Given a terminal point determined by a real number t, determine the values of the trigonometric functions above evaluated at t.
- State the signs of sine, cosine, and tangent in each of the 4 quadrants of the coordinate plane.
- Use the procedure in the grey box on page 412 of Stewart, Redlin, and Watson to evaluate the trigonometric functions at any real number.
Section 5.3: Trigonometric Graphs
- Relate the graphs of sint and cost to the terminal point (x,y) a distance t from the point (1,0) along the unit circle.
- State what property a function must have to be periodic.
- State the period of sint and cost.
- Sketch one period of the graphs of sint and cost.
- Identify the amplitude and period of the functions s(t)=asink(t−h) and c(t)=acosk(t−h).
- Explain the impacts of a, k, v, and h on the transformations s(t)=v+asink(t−h) and c(t)=v+acosk(t−h) of sint and cost, and how they impact the graphs of the transformations.
- Identify the functions s(t)=v+asink(t−h) and c(t)=v+acosk(t−h) from a graph of a single period.
- Identify the domain and range of the functions sint, cost, s(t)=v+asink(t−h), and c(t)=v+acosk(t−h).
Section 5.4: More Trigonometric Graphs
- State the period of tant, cott, sect, and csct.
- Sketch one period of tant, cott, sect, and csct.t
Section 5.6: Modeling Harmonic Motion
- State the equation for simple harmonic motion, and identify the amplitude, period, and frequency given the equation for simple harmonic motion.
- Relate the angular frequency k of a sine wave to its temporal frequency, which we will denote by either ν (the lowercase Greek letter nu) or f. Your textbook calls temporal frequency simply ‘frequency’.
- Identify the unit of frequency in the International System of Units.
- State the equation for simple harmonic motion.
- State the model for the displacement of a mass on a spring from its equilibrium position and identify the period, frequency, and amplitude of the mass’s motion.
- Identify a model for a pure tone (sound), and identify how its parameters are related to loudness and tone.
- Relate the frequency of a tone to the frequency of its octaves.