Assessment for Identities

Objective

SWBAT use identities to verify other identities and evaluate trigonometric functions

Big Idea

Through a written assessment students demonstrate their proficiency in using trigonometric identities to verify identities and evaluate trigonometric functions.

Lesson Author

Katharine Sparks

Independence, MO

Grade Level

Eleventh grade

Twelfth grade

Subjects

Math

Standards

HSF-TF.A.3

(+) Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosines, and tangent for x, π + x, and 2π – x in terms of their values for x, where x is any real number.

HSF-TF.C.8

Prove the Pythagorean identity sin<sup>2</sup>(θ) + cos<sup>2</sup>(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.

HSF-TF.C.9

(+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

MP1

Make sense of problems and persevere in solving them.

MP2

Reason abstractly and quantitatively.

MP3

Construct viable arguments and critique the reasoning of others.

MP5

Use appropriate tools strategically.

Assessment

45 minutes

For this assessment students are allowed to use the reference sheet they developed during the unit. The one shared was typed by a students and shared with anyone that wished to have the sheet.

I allow the use of the identity sheet because the main goal of this unit is for students to use the identities. I also teach calculus and I find that the students know the important identities even though I do not have them memorize them for this test.

On this test, I do allow students to get a hint on the first 2 questions if they get stuck. I will deduct points by determining how much of a hint the student needed. Correcting a sign error is not as much of an error as reminding students of the property needed to start the problem.

Question 3 on the test allows students to show their reasoning. I did not state which formula to use so the students can solve it many different ways.

Students sometimes struggle with question 4. I made cos B=-3/4 to make sure students realize that just because you see a 3 and a 4 the other side (y in this case) is not necessarily 5. That is a common error. The other error is simplifying with radicals. Some students are not sure how to write (3)(-sqrt21). We have briefly reviewed this in class but many panic on tests and forget what happened on homework.

On the last 2 problems students struggle with computations with fractions. This is an issue I work on throughout the course. I try to work with students on an individual basis to fix the errors or misconceptions.

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