Evaluating Trigonometric Functions
Lesson 8 of 13
Objective: SWBAT find the value of trigonometric functions in the coordinate plane
Today I want to put together everything we have done over the last several lessons. I begin this effort by asking students to work a problem. Students work together to determine the answers. I move around and ask guiding questions including:
- What does the prompt state? Are you confused about anything in the prompt? (some students will need help on literacy techniques of breaking the question down and writing ideas out)
- How many answers will you have?
- Will a diagram help?
- Identify the angle. How did we deal with angle such as this when we did the Sine and Cosine Activity?
- Is the radius 1?
- How can you find the radius?
After about three minutes I will begin to identify students to post their answers. After the answers are shared, I will ask for questions, giving students more time to review the answer and think about their work.
Looking at the board, I will focus my attention on answers that have been (or have not been) rationalized since some of my students may think answers are wrong if they are not exactly the same as what is on the board. If a student asks about such an answer, I will begin by saying, "Did you check to see if your answer is an equivalent quantity?"
As necessary, I will recall a student to the board to ask them to draw the diagram he/she used to help with the problem. (I made note of how students were using diagrams when I chose them to share their answers.)
I continue with finding the value of trigonometric functions of special angles. I give students some trigonometric functions to evaluate. I make sure to use the term evaluate. If students are slow to get started, I'll prompt them with some questions about the meaning of evaluate and the concept of equivalent expressions. I expect that some students will think that evaluate means "to find the degree equivalent for the angle." Students see the term evaluate used in many contexts, and sometimes they overgeneralize the meaning to a specific type of problem. For example, they may fix their attention on its use with function notation like "evaluate f(x) when x=3", which can be hinder them in trigonometry and calculus.
I also work with the class to see how they can find the answer. I remind the students that they have a unit circle that may help or they can draw a diagram and find the ordered pair on the terminal side of the angle to find the value. Some students will need more help than others. When I do an example on the board I will do both methods.
Questions I ask as students work include:
- Which quadrant is the terminal side of the angle?
- Because it is in this quadrant what will be negative? (thinking x or y)
- Does the trigonometric function involve x, y or both?
- Will your answer be positive or negative?
Now that the main ideas for this lesson have been introduced, I give my students two worksheets to continue practicing finding trigonometric values.
- Special Angles Worksheet 1 focuses on the speial angles.
- Finding Trigonometric Values on the Coordinate Plane worksheet has a circle with ordered pairs on the circle students will find values and then Students will work on these worksheets today.
As students work I clarify and reteach students. Many of my students will struggle with the second page of Finding Trigonometric Values on the Coordinate Plane. The questions ask students to consider ideas that are not quick answers. As the students think about the questions they are discovering how the properties of even and odd functions connect to the trigonometric functions. This concept will be used more when we verify identities.
As we end class today I have the students evaluate tan(pi/2) and put the answer on an Exit Slip. I have not spent much time how to write if a function is undefined. This informal assessment will let me see if student realize the function is undefined. Some students get confused with 1/0 and 0/1. Any students that answer the question as 0 will need some review on this issue.