More Trig Functions

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Objective

SWBAT evaluate and define other trigonometric functions in terms of Sine and Cosine.

Big Idea

Students use their knowledge of Sine and Cosine to evaluate Tangent, Cotangent, Secant, and Cosecant.

Warm-up: Graph Match

10 minutes

As a warm-up today, I am going to have students do the Sin Cos graph match. In this activity, students should sketch the sine or cosine curve and use the graph to identify which value matches. No calculators allowed! I think this activity is a good way to remind students that the functions represent values at each point along the curve. It is also requires students to use their reasoning and logic skills.

Today, I will only have students work on matching #1 and #2. The graphs #3 and #4 are too difficult as they have not studied the graphs of secant and cosecant yet. I like to turn this activity into a little competition. The first team to bring me all the correct answers wins! I give each graph separately. The real completion gets going on graph #2 after we go over graph #1 and students see how they can logic these problems out.

Explanation: Other Trigonometric Functions

35 minutes

In the middle part of today’s lesson, I am going to finally formalize the other trigonometric functions that we have yet to discuss. When presenting page 2 of today’s Other Trig Functions_flipchart, I will have students copy down the definition of the other trig functions in terms of sine and cosine. Most of this lesson will center on students being able to evaluate these trigonometric functions for given angle values. In this course, we do not study the graphs of the other trig functions but in theory students should be able to derive them based on the other skills they will learn in this lesson and have already learned about graphing sine and cosine curves.

Pages 3-8 of the flipchart, ask students to practice evaluating the new trig functions at special angles using the unit circle. I like to have students try the problem and then I go over briefly how to obtain the answer. By the 3rd or 4th question I have most of the class answering them correctly.

Page 10 of the flipchart establishes the fact that some of these functions are undefined at certain angle measures, reminding students that we can never divide by zero. Pages 11-12 include clicker questions to reinforce this idea and check for understanding.

Pages 13-18 of the flipchart focus on the face that the signs of these functions are dependent on the sine and/or cosine functions. When presenting page 13, I like to go through a few examples with students verbally. “If sine is negative and cosine is positive, what is tangent? If sine is positive and cosine is negative, what is secant?”

Closure: 3-2-1 Assessment

5 minutes

To close out this unit, I want students to complete a 3-2-1 Assessment before they leave. I will ask students to identify 3 things they learned this unit, 2 specific things they are still confused about, and 1 question they still have about this unit.  

Homework

Tonight I will assign students Homework 11- Trigonometric Functions