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

==>

Read the phase shift from the graph

==>

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

==>

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.

==>

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:

==>

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)