review test 3 math 1330 test 3 review sections 4.1-4.3, 5
TRANSCRIPT
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Review Test 3
Math 1330
Test 3 Review
Sections 4.1-4.3, 5.1a, 5.2-5.4
Example 1:Let θ be an acute angle of a right triangle and that
. Find all the
rest of the trigonometric functions of θ.
Example 2:Let θ be an acute angle of a right triangle and that
. Find all the
rest of the trigonometric functions of θ.
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Review Test 3
Example 3:A sector of a circle has central angle θ = 2π/3 and area 16π/3 ft2.
a. Find the radius of the circle.
b. Find the length of the sector for the problem above.
Example 4: Find the area of the sector with a central angle of θ = 240° and a r = 6 cm
Example 5: A car has wheels with a 10 cm radius. If each wheel’s rate of turn is 3
revolutions per second
a. What is the angular speed?
b. How fast is the car moving in units of cm/sec, (linear spead)?
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Review Test 3
Example 6: Find three angles, two positive and one negative, that are coterminal with the
given angle: 3
4
Example 7: Evaluate the following.
3
4sin
6
5tan
3
2cot
4
5cos
6
5sec
3csc
Example 8: Simplify
a.
3
14sin
b.
3
16tan
c.
4
17cot
6
34cos4
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Review Test 3
Example 9: Fill in the unit circle
Example 10: Evaluate
32
1sin 1
1tan 1
3cot 1
3
32sec 1
2csc 1
2
1cos 1
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Review Test 3
Example 11: Evaluate
7
3coscot 1
Example 12: Find the amplitude, period and phase shift.
x3
1cos4
2
3
3
2sin
2
1 x
x
5
1sin6
x
2
1cos5
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Review Test 3
Example 13: List all the x-intercepts for
3
14cos4 xy
on the [-π/6, π/2]
Example 14: Write a cosine function with a positive vertical dilation, given the amplitude is
3, the phase shift is 3 to the left, the vertical shift is 2 up, and the period is 2.
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Review Test 3
Example 15: Sketch the following functions: Label, for one period, x-, y-intercepts as
ordered pairs; max value(s), min value(s) as ordered pairs.
f (x) = -3sin(4x).
g(x) = 7 cos(5x)
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