then a + b is equal to
a)
b)
c)
d)
e)
Solution:
The asymptotes of the tangent function y = tan q are at the zeros of cos(q)
Therefore, the asymptotes are obtained when
Mcad reset:
Solve for x
Create a table to compute x for different values of k
Consider that the graph represents a sine function a sin (bx + c) shifted to the left.
Read the amplitude from the graph.
Compute the period
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Read the phase shift from the graph
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Thus, the function is
Section 5.6
5.6.1 (001-T2-12)
If x = a and y = b are the 2 asymptotes of
in the interval
or
Multiply by . This will cause the inequalities to reverse directions
or
add 1 to both sides
Thus, the range in interval notation is b) R = (- , -1/2] U [5/2, )
Find the smallest positive angle coterminal with the angle .
Verify the identity
Find the values of x and y such that
A wheel is rotating at 100 revolutions per minute, find the angular speed in radians per second.
Sketch the graph of
If , b > 0, period = 6 and f(3) = 4, find
The first and the last rows are not inside the given interval.
So, in the interval , the asymptotes are at and
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Graph of
5.6.2 (001-T2-13 $5.6)
The range and the period of are:
a) R = (- , -1/2] U [5/2, ) , P = p/3
b) R = (- , -1/2] U [5/2, ), P = - p/3
c) R = (- , -1/2] U [5/2, ), P = 2p/3
d) R = (- , -3/2] U [3/2, ), P = 2p/3
e) R = (- , -5/2] U [1/2, ), P = 2p/3
Solution:
The period =
a)
b)
c)
d)
e)
Solution:
5.2.2 (001-T2-14 $5.2)
The top of a radio antenna is 100 m high from the ground. A wire 200 m long is attached to the top from the ground. What is the angle the wire makes with the ground.
a)
b)
c)
d)
Solution:
5.2.3 (002-Final-2 $5.2 )
a)
b)
Math002
Solution of Old Exams Problems

Chapter 5
A. M. Farhat
Section 5.1
5.1.1 Covert the angle radians to revolutions
Solution:
Multiply by the conversion unity
5.1.2 (011-T1-9)
A wheel of a truck has a radius 1.6 feet.
a) How far will the truck move if the wheel turns through 40o ?
q in radians
b) If the wheel is rotating at the rate of 6 revolutions per second, find the speed of the truck in feet per second.
Section 5.2
5.2.1 (001-T2-10 $5.2)
The value of the expression is equal to:
Solution:
Since the angle is negative, we find the coterminal angle using equation:
coterminal angle =
See lecture notes: Computing the coterminal angle.
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To find k, divide over 2 p
coterminal angle =
Thus,
Section 5.5
5.5. 1 (001-T2-2 $5.5)
The adjacent graph represents, over one period, the following function:
a)
b)
c)
d)
e)
Solution:
c)
d)
e)
Solution:
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Solve for y
Let x = -4 ==> y = 3
Choose a negative value for x and compute y.
==>
Compute the hypotenuse
Section 5.4
5.4.1 (001-T2-15)
The rectangular coordinates of the point on the unit circle is:
a)
b)
c)
d)
e)