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Solving Trigonometric Equations using Sum and Difference Formulas

Solve sine, cosine, and tangent of angles that are added or subtracted.

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Solving Trig Equations using Sum and Difference Formulas

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.

1.

2.

3.

Explore More

Solve the following trig equations in the interval .

1. 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?

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