Pre-Ap Pre-Calculus 1st Semester Exam Review With Answers - Varsity Math, Coach G - 2015 Page 2
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13Pre-AP Pre-Calculus
The original Ferris wheel, built by George Ferris for the 1893 World’s Fair, was much
18.
larger and slower than its modern counterparts. It had a diameter of 250 feet and
contained 36 cars, each of which held 40 people. It made one revolution every 10
minutes and reached a maximum height of 264 feet. Grover Cleveland was given a
private ride. He got on and the wheel starting slowly turning.
a.) Sketch a graph of this sinusoid.
b.) Write an equation expressing Grover’s height above the ground in terms of time (in
minutes) since the Ferris wheel started turning.
c.) How high was Grover after 16 minutes?
th
d.) When was he 200 feet above the ground for the 4
time?
BACK TO NON-CALCULATOR!
V
ERIFYING TRIG IDENTITIES AND SOLVING TRIG EQUATIONS
19.
Simplify: cos x + sin x tan x.
Simplify: (1 – cos x) (csc x + cot x).
20.
2
2
sin
x
cos
x
21.
Simplify:
.
tan
x
2
22.
Verify: sin
x sec x csc x = tan x
1 cos 2
x
23.
Verify:
tan
x
.
sin 2
x
24.
Find all 6 exact trig values for 75
.
4
3
A and is in quadrant 2, and
B
25.
If
sin
cos
and is in quadrant 3, find the following:
5
5
sin (A + B) = _____
cos (A + B) = _____
tan (A – B) = _____
sin 2A = _______
cos 2B = _______
26.
Solve on the interval [0, 2): -2 cos x =
2
Solve 2 csc x – 4 = 0 for [0, 2).
27.
2
x – 1 = 0 for [0, 2).
28.
Solve 4 cos
29.
Find ALL solutions of 2 sin x = 3 .
3 tan 2x = 1.
30.
Find ALL solutions of
31.
Solve and give the principal value of x for 4 tan x + 4 = 0.
O
T
E
T
I
THER
RIG
QUATIONS AND
RIG
NVERSES
32.
Which of the following functions are one-to-one?
2
3
3
sinx
cosx
tanx
cotx
secx
cscx
x
x
x
|x|
x
x
33.
a. Graph the parent functions for y = csc x, y = sec x, y = tan x, and y = cot x. Give the
period of each.
b. Graph the three trig inverse functions. List the domain and range of each.
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