Therefore,

where k is the quotient of the division

Since the angle A is negative, the coterminal c is obtained by the formula

Solution

See lecture notes: "Computing the Coterminal Angle."

a)

1. Find the coterminal angle of the angles

Quiz 4-03

Note: Mathcad uses the function

log(x,b) for logbx

Mathcad solution:

Note: ==> x = 3 or x = -3. However, -3 is rejected since the base has to be greater than one.

==>

Solution:

3. Solve for x:

Mathcad Solution

È È (1, ¥)

Thus, the solution is

So, the interval is a good one, i.e., every point in this interval will satisfy the inequality. Next, we choose every other interval. Thus, we leave the interval (-4, -1) and take the interval with the exclusion of the point 1.

The two intervals surrounding the point 1 is considered as one region because it is coming from a factor raised to an even power. So, we basically have three intervals: , (-4, -1) and (excluding the point 1)

Choose a point in any interval, say x = -100 and substitute into the inequality to check for the sign:

Check using Mathcad:

So,

Solution

b)

But is not defined because

So,

Therefore, the coterminal angle is

First, we find the coterminal angle

Solution

a)

2. Find the values of

Therefore,

Where k is the quotient of the division

Since the angle b in positive and is in degrees, the coterminal angle c is obtained by the formula

b)

Mathcad solution

Note:

This method works well provided that non of the factors is raised to an even power. If this is the case, then the two intervals surrounding the zero of that factor is considered as one region because there will not be a change of sign around this point.

(-1, 0) È (1, )

Thus, the point x = 100 satisfies the inequality and every point in that interval will also satisfy the inequality. Now, every other region will also satisfy the inequality. Hence, the domain is:

Non of the points is part of the domain since we do not have equality.

Pick a region and choose any value in that region, say x = 100, which lies in the interval (1, ). Substitute x = 100 into the inequality to check for the sign. Here we have,

Therefore, the roots (zeros) are: 0, 1, and -1. These points divide the real line into four intervals as shown below:

Factor and set greater than 0

The domain is obtained by setting the argument greater than zero and solving the inequality for x

Solution:

Find the domain of the function

Quiz 2-03

Select the points to plot

Solution:

Sketch the graph of the function

Or,

Sketch the graph of the function

Quiz 1

Solution of Quizzes

Math002-033 (A. Farhat)

and

The zeros are

Solution:

2. Find the domain of

Mathcad solution:

Therefore , the solution is x = -5

Submitting x = -5 into the original equation, we find that it satisfies the equation. But x = -10 will result in a negative argument for the log.

Solution:

1. Solve for x

Quiz 3-02