Thus,

So, now we look for the angle in quadrant I or quadrant II whose cosine is . That angle is (see Figure 2)

Figure 1

Using the unit circle, we have (see Figure 1)

We know that but only if x is in the range of . That is, only if . Therefore, we can not use this property (this is not to say that we can not find the value).

Solution:

31+. Find the exact value of

Mcad check:

Therefore,

So, we look for the angle in the quadrant I or quadrant IV whose sine is . The angle is

==>

Recall that if x is in the domain of , that is, if or then

Solution:

11. Find the exact value of

More to be added later

Therefore,

==>

The logical choice should be the second one because cos ( ) is readily available by applying the cosine to both sides of equation (1).

or

or

This means that we are looking for cos (2q). To find cos (2q ), we have three choices:

(1)

Let

Solution:

50+. Find the exact value of

Figure 2

Mcad check:

Here, it is better to start with the right-hand side.

Solution:

33. Verify the identity

Solution:

27+. Verify the identity

Multiply and divide by

Solution:

21. Verify the identity

Solution:

13. Verify the identity

6.1

Most of the problems are selected from the textbook. They are usually the ones that precede a homework problem. The intention is to give the student a close example to help him solve the homework assignment. If the homework problem and the one preceding it are not similar, another problem is created and a (+) sign is added to the number of the problem.

Solution of Homework Problems Minus One

Chapter 6

6.2

take as a common factor

take cos(x) as a common factor

take 2 as a common factor

using the identity

Using the expansion where

Start with the left-hand side and regroup as follows:

Solution:

63+. Verify the identity

Solution:

41. Verify the identity