## Reflection: Lesson Planning Solving Basic Trigonometric Equations - Section 2: Explanation

After talking with some other Master Teachers in this project, I learned that some teachers prefer to teach solving basic trig equations by having students take the inverse of both sides of the equation regardless of the value being positive or negative. Then this will give one angle that satisfies this equation, and then students use this information to find their second angle.

Confused? Look at these Examples of Two Different Methods. Method one is what is used in the notes presented in this lesson. Method 2 is the other method that I realized some teachers use.

Method 1

Benefits:

- It works for every kind of basic trig equation. Whether ratios are positive or negative and functions are sine, cosine, or tangent this method will always be worked out using the same steps.

- It solidifies students’ understanding of reference angles and the fact that the absolute values of trig functions remain the same at the same reference angles.

Potential Drawbacks:

- Students overgeneralize and think that trigonometric ratios cannot be negative.

- They don’t realize they can take the inverse of a negative value to obtain one solution for x.

- Students incorrectly think that the reference angle is a solution when it is actually not

Method 2

Benefits:

- Follows students’ natural instinct to take the inverse of both sides to isolate for x.

- I like this method when we have the ‘nice’ ratios that work with the unit circle because students can use the unit circle to find the second angle.

- Emphasizes the concept of an intersection point of a solution on the unit circle which is great for estimation of other values of trig ratios which are not derived from special triangles .

Potential Drawbacks:

- This process can get confusing when finding the second solution on this interval. Look at example 1 and 2 for method 2. Students still have to find their reference angle eventually to be able to calculate the second solution. This seems like an extra step to me. This may become more difficult for students when we get to ratios that are not derived from special triangles. For example, if students had to solve.

- Also, when looking at the cosine function students may generalize that they can find the other angle by subtracting the first angle from zero. This works for the cosine function, but not the sine function.

You may want to show your students both methods as we progress through the notes. In example 2, they are directed to use method 1. However, in example 3 you may want to show the other method. I personally did not show this method at this time.

Lesson Planning: How do you approach solving basic trig equations?

# Solving Basic Trigonometric Equations

Unit 9: Trigonometric Equations
Lesson 8 of 16

## Big Idea: Students solve basic trig equations and face a great challenge in finding ALL the solutions by playing Around the World.

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2 teachers like this lesson
Standards:
Subject(s):
Math, Precalculus and Calculus, Trigonometry, Trigonometric Equations, Solving Basic Trig Equations, PreCalculus, 12th Grade
55 minutes

### Tiffany Dawdy

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