Exam 3 Suggested Study Problems MATH 1060Q, December 2008
Not everything on the following list will appear on the examination but many of
these ideas and skills will be tested there. Some of these items will appear on the final exam.
- Find the inverse of an algebraic function.
Sample: If f(x) = (x + 3)/(x - 1),
find the formula for f (-1)(x).
- The Wrapping Function and the trigonometric point P(t).
Unit circle definitions of cosine and sine
Samples: Page 193, #27; p. 205 #51.
- Knowledge of the values of sine, cosine, etc., at integer multiples of π/2, π/3,
π/4, π/6
- Finding reference angle and using it (plus quadrant) to evaluate
a trigonometric function
Samples: Page 205 #9, 11, 13, 15.
- Given a point on its terminal ray, calculate the sine and cosine
of an angle in standard position.
Sample: If θ is an angle in standard position and the point
(3, -8) is on its terminal side, find the values of the six trigonometric functions
at θ.
- Periodicity and symmetry properties of the trigonometric functions
Sample: If
cos u = 1/9, what are cos(u + 25π) and cos(u + 26π)?
- Properties of inverse trigonometric functions
Samples: Page 251 #15 17, 19, 29, 34, 41, 42.
- Right triangle trigonometry: See the homework set for ¶ 4.7.
- Amplitude, period, and graph of f(x) = A
sin(Bx)
Sample: Find the period of g(x) = cos(1060 x) and sketch the graph
of g for one period. Label all significant points with their coordinates.
- Applying the Pythagorean identities
If csc²(t) = 4, find tan²(t)
- The sine and cosine of a sum or a difference of inputs
Samples: Express sin(x + π/3) and cos(x + π/3).
- Double angle formulas.
Samples: Find the exact values of sin(2t), cos(2t), and tan(2t) if sin(t) = 1/3 and the point P(t) is in the first quadrant.
Find sin(2x) and cos(2x) if x is the radian measure
of the angle opposite the smallest side in a 5, 12, 13 right triangle .
- Half angle formulas.
Samples: Find the exact values [not calculator approximate values] of
sin²(π/8), cos²(π/8), tan²(π/8), and sin²(π/12), cos²(π/12), tan²(π/12)
.
- Law of Sines, SSA data
Sample: In triangle ABC with the standard labeling, suppose that a = 1.8, b = 2, and
∠ α = 40 degrees. Find the possible values of ∠ β and ∠ γ.
- Law of Cosines, SSS data
Sample: Find the cosine of the angle opposite the smallest side of a
triangle with sides of length 5, 6, 10.
- Continuously compounded interest.
Sample: Page 286 #35d.
- Apply properties of exponentials and logarithms.
Sample: Page 296 #1-11 odd.
A list of trigonometric formulas, including some of
the identities, will be given on Page 1 of the exam. Some but not
all of these will be useful in working certain problems on the
test.
Calculators must be used on the exam. But you must still know
the basic facts about sin(π), cos(π/4), etc., exactly -- you
will be marked as wrong if a problem asks for an exact answer --
in terms of mathematical constants such as π, the square root of
23, etc. -- and you use a calculator approximate value.
Good luck on the exam!