Chapter 2
Trigonometry Review
I
n addition to having a strong algebra background, you need a strong trigonometry skill
set for calculus. You want to know the graphs of the trigonometric functions and to be
able to evaluate trigonometric functions quickly. Many calculus problems require one or
more trigonometric identities, so make sure you have more than a few of them memorized
or at least can derive them quickly.
The Problems You’ll Work On
In this chapter, you solve a variety of fundamental trigonometric problems that cover topics
such as the following:
✓ Understanding the trigonometric functions in relation to right triangles
✓ Finding degree and radian measure
✓ Finding angles on the unit circle
✓ Proving identities
✓ Finding the amplitude, period, and phase shift of a periodic function
✓ Working with inverse trigonometric functions
✓ Solving trigonometric equations with and without using inverses
What to Watch Out For
Remember the following when working on the trigonometry review questions:
✓ Being able to evaluate the trigonometric functions at common angles is very important
since they appear often in problems. Having them memorized will be extremely useful!
✓ Watch out when solving equations using inverse trigonometric functions. Calculators
give only a single solution to the equation, but the equation may have many more
(sometimes infinitely many solutions), depending on the given interval. Thinking about
solutions on the unit circle is often a good way to visualize the other solutions.
✓ Although you may be most familiar with using degrees to measure angles, radians are
used almost exclusively in calculus, so learn to love radian measure.
✓ Memorizing many trigonometric identities is a good idea because they appear often in
calculus problems.
Trigonometry Review
I
n addition to having a strong algebra background, you need a strong trigonometry skill
set for calculus. You want to know the graphs of the trigonometric functions and to be
able to evaluate trigonometric functions quickly. Many calculus problems require one or
more trigonometric identities, so make sure you have more than a few of them memorized
or at least can derive them quickly.
The Problems You’ll Work On
In this chapter, you solve a variety of fundamental trigonometric problems that cover topics
such as the following:
✓ Understanding the trigonometric functions in relation to right triangles
✓ Finding degree and radian measure
✓ Finding angles on the unit circle
✓ Proving identities
✓ Finding the amplitude, period, and phase shift of a periodic function
✓ Working with inverse trigonometric functions
✓ Solving trigonometric equations with and without using inverses
What to Watch Out For
Remember the following when working on the trigonometry review questions:
✓ Being able to evaluate the trigonometric functions at common angles is very important
since they appear often in problems. Having them memorized will be extremely useful!
✓ Watch out when solving equations using inverse trigonometric functions. Calculators
give only a single solution to the equation, but the equation may have many more
(sometimes infinitely many solutions), depending on the given interval. Thinking about
solutions on the unit circle is often a good way to visualize the other solutions.
✓ Although you may be most familiar with using degrees to measure angles, radians are
used almost exclusively in calculus, so learn to love radian measure.
✓ Memorizing many trigonometric identities is a good idea because they appear often in
calculus problems.