Math 112 – Review for Exam 2
Your second exam is coming up on Friday, Nov. 14. You may bring one 3-inch by 5-inch note card with notes on
both sides. If you bring in a larger card, I will cut it down to 3-inches by 5-inches. You will have 50 minutes for
this test. Practice problems until you are comfortable. I will provide the attached sheet of identities, so you won’t
need to clutter your own note card with those items.
Section 4.1
 Be able to plot one period of the sine or cosine curve of the form y   A sin( Bx) or y   A cos( Bx) .
Use the method we discussed in class to set up a nice scale, create four equal regions, and plot the five
key points. I will be looking for support work that shows you can use the method I taught you.
 Know what amplitude is and how to find it. Know that amplitude is a distance so it is a positive number.
 Know that the B value is NOT the period. It indicates that there is a period change. Be able to calculate
the new period.
 Expect to be given the picture of a graphed sine or cosine curve and you will build the equation.
Any problem in this section from 11-22, 25-40, and 53-60 would make great test questions.
Section 4.2
 Know what an even function is, which trig functions are even, and how to simplify an expression using
that idea.
 Know what an odd function is, which trig functions are odd, and how to simplify an expression using that
idea.
 Know how to graph one period of a sine or cosine function that involves vertical translations and/or phase
shifts.
 You will likely be given a equation of a sine or cosine function with an amplitude change, period change,
vertical shift, and phase shift. Be able to identify each and be able to make a nice sketch that lays out four
equal regions and five key points.
 Expect to be given the picture of a graphed sine or cosine curve that involves a phase shift as well as other
changes and you build the equation.
Any problem in this section from 9-24, 25-36, 47-50 would make great test questions.
Section 4.3
 Know that the tangent function has a period of . If there is a period change then calculate the new period
by computing


.
B
Be able to look at the graph of a tangent function and identify the period, phase shift, and vertical
asymptotes.
 Be able to sketch one period of a tangent function that contains a vertical stretch or shrink, period change,
or phase shift. Be sure to calculate the new vertical asymptotes and new period. Then break up the
period into four equal regions and plot the three key points.
Any assigned problem from this section would make a good test question.
Section 5.1
 Be able to verify any of the identities from the homework. Make sure you do NOT do anything to both
sides. When you verify an identity, you start on one side and show all your steps until you make it look
like the other side. You might need to switch to all sinx and cosx, add fractions, use other identities,
factor, distribute, etc. I will want to see EVERY step. Some of you made magic leaps without showing
enough steps.
You will have to verify an identity for sure so be sure you can work through all the assigned problems from
this section.
Section 5.2
 Use sum and difference formulas to find exact values as in the section examples 1, 3, and 5.
 Never give decimal answers. I want to see all your fraction and square root work.
Any assigned problem would make a great test question.
Section 5.3
 Use double-angle identities to find exact values as in examples 1and 2.
 Be able to verify an identity that involves the double-angle identity (Problems 23 through 28).
Any assigned problem would make a great test question.
Section 5.4
 Use half-angle identities to find exact values as in examples 1, 2, and 3.
 Remember that the half-angle identities that involve ± do not know the sign of the final answer. It is up to
you to know the quadrant in which the angle falls so you can figure out the correct sign.
Any assigned problem would make a great test question.
Section 6.1
 We used inverse trigonometric functions earlier this term when finding angles. We learned more about
inverse functions in this section. Pay CLOSE attention to what the inverse sine, inverse cosine, and
inverse tangent functions hand you. The inverse sine function will NEVER spit out an angle of 150, for
example. Do you know why? Be aware of the restrictions for each inverse function. Look at the
summary in the blue box at the bottom of page 337. It reminds you of the output (range) values for each
inverse function.
ANY problem in this section from 1 to 88 would make a great test question. Practice the odd problems and
check your answers. Make sure you are getting these correct. They are simple in general…but the
restrictions involving the output can make these confusing.
Section 6.2
 We learned how to solve equations that involve one type of trigonometric function. We discussed three
main categories of these types of equations:
 There were simple equations in this section, as in Example 1(a), Example 2, and Example 4. Isolate the
trigonometric expression and use the unit circle to find all solutions or use the reference angle to build
solutions in appropriate quadrants.
 There were equations involving a double angle that needed some special care like in Example 1(b) and
Example 3.
 Finally we discussed equations that involved squares of trig functions. These are quadratic in nature and
require factoring or the use of the quadratic formula to solve. Study Examples 5, 6, and 7 in the section.
Any assigned problem would make a great test question.