Math 131 Sections A & B 1/24/06
Lab 1 – Review of Trigonometry
The purpose of this lab is to review trig so that it you may use it in the study of calculus. These exercises may lead to other questions. Feel free to explore those with your group during your review. Each group can turn in one report. Sketches should be on graph paper.
I. Right-triangle definitions.
1. Find the following given the right triangle in the sketch.
13
cos A = ______sec A = ______5
12 A sin A = ______csc A = ______
tan A = ______cot A = ______
2. Solve the triangle given that tan A = 3 and c = 12.
3. Draw triangles for the following:
a) Find the exact functional value of cos[sin-1(5/13)].
b) Write tan(cos-1w) as an algebraic expression in w.
II. Unit Circle definitions.
1. What does it mean for an angle to be in standard position?
2. Let t be an angle in standard position. What is the relationship between s(t) = sin t and the unit circle?
What is the relationship between c(t) = cos t and the unit circle?
3. What are the standard reference angles?
In degrees:
In radians:
You should know the values of the six trig functions at any angle that has a standard reference angle. That means that you do not need a calculator to find these values. This knowledge should let you bound or estimate the values at other angles.
4. Sketch the angle. Evaluate the function at the given angle without a calculator. (e.g. cos 90o = 0)
cos sin tan
tan cos sin
sin 135o tan 300o cos 180o
III. Graphs of Trigonometric Functions
1. Within your group, do “quick sketches” of at least 2 periods of the six basic trig functions (by hand).
2. Give the amplitude, period, & phase shift. Sketch the graph.
a)
b)
c)
3. State the rule of a function of the form f(t) = A sin( bt + c) or g(t) = A cos( bt + c) for the graph.
(see #18-28, sec 1.5)
IV. Other
1. What is your favorite trig identity?
2. Text, section 1.5 problems 36, 37, 39, 42