As Agent Trigonometry, you are now given another piece of the puzzle: . What is the value of ?

### Guidance

Lastly, we can use the sum and difference formulas to solve trigonometric equations. For this concept, we will only find solutions in the interval .

#### Example A

Solve .

**Solution:** Use the formula to simplify the left-hand side and then solve for .

The cosine negative in the and quadrants. and .

#### Example B

Solve .

**Solution:**

In the interval, and .

#### Example C

Solve .

**Solution:**

At this point, we can factor the equation to be . , and 1, so . Be careful with these answers. When we check these solutions it turns out that does not work.

Therefore, is an extraneous solution.

**Concept Problem Revisit**

In the previous lesson you solved the expression as:

So what you're now looking for is the value of where .

The cosine of is equal to .

### Guided Practice

Solve the following equations in the interval .

1.

2.

3.

**Answers**

1.

2.

3.

### Explore More

Solve the following trig equations in the interval .

**Real Life Application**The height, (in feet), of two people in different seats on a Ferris wheel can be modeled by and where is the time (in minutes). When are the two people at the same height?

### Answers for Explore More Problems

To view the Explore More answers, open this PDF file and look for section 14.14.