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# Formative Assessment: Simplifying Identities and Trig Formulas

Lesson 7 of 15

## Objective: SWBAT demonstrate knowledge of trig identities and formulas.

## Big Idea: A formative assessment will gauge the students' understanding of these trig relationships.

*50 minutes*

#### Check Homework

*15 min*

Students usually have difficulty on the second part of question 3 on yesterday's quiz review. If students ask about it, I will choose a student who did get it correct and have them show their work. When writing cos(arcsin 1/4 + arccos 3/4) as an algebraic expression, students may not realize that arcsin(1/4) and arccos(3/4) are two separate angles. My students sometimes try to represent both of these angles by drawing one triangle and then getting confused when they realize that it is impossible for an angle to have a sine of 1/4 and a cosine of 3/4.

Other students don't see the need to use the cos(A + B) formula for this problem. Reminding them that arcsin(1/4) and arccos(3/4) represent angles will help to solidify this fact.

#### Resources

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#### Quiz

*35 min*

Here are some sample problems that you may choose to use for your quiz over this portion of the unit. More than anything, this formative assessment will give students practice with the formulas and will assess their progress. Typically, students will know the formulas well, but will forget a negative sign here or there.

For question 1, I will usually have a few students who have major misconceptions and will evaluate cos(-12/13) thinking that -12/13 is the angle measure. Other students may distribute the cosine to A and B to get cos*A* - cos*B*. This is a good time to intervene with these students so that they can get clarification before the unit assessment. I discuss this more in the video below.

#### Resources

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- UNIT 1: Functioning with Functions
- UNIT 2: Polynomial and Rational Functions
- UNIT 3: Exponential and Logarithmic Functions
- UNIT 4: Trigonometric Functions
- UNIT 5: Trigonometric Relationships
- UNIT 6: Additional Trigonometry Topics
- UNIT 7: Midterm Review and Exam
- UNIT 8: Matrices and Systems
- UNIT 9: Sequences and Series
- UNIT 10: Conic Sections
- UNIT 11: Parametric Equations and Polar Coordinates
- UNIT 12: Math in 3D
- UNIT 13: Limits and Derivatives

- LESSON 1: Trigonometric Identities - Day 1 of 2
- LESSON 2: Trigonometric Identities - Day 2 of 2
- LESSON 3: Student Work Day and Individual Conferences
- LESSON 4: Does cos(A - B) = cos(A) - cos(B)?
- LESSON 5: If sin(A) = 3/5, what is sin(2A)?
- LESSON 6: Formative Assessment Review
- LESSON 7: Formative Assessment: Simplifying Identities and Trig Formulas
- LESSON 8: What is cos(22.5°)?
- LESSON 9: Solving Trig Equations
- LESSON 10: Using Formulas to Solve Trig Equations
- LESSON 11: Extraneous Solutions
- LESSON 12: Putting All of the Pieces Together
- LESSON 13: Formative Assessment: Solving Trig Equations
- LESSON 14: Unit Review Game: Lingo
- LESSON 15: Unit Assessment: Trigonometric Relationships