Discovering Trig Identities (Day 4 of 4)

Objective

Students will be able to visualize and interpret the trigonometric identities with a focus today on the pythagorean identities.

Big Idea

Students use TI-Nspire calculators to develop their own understandings of what trigonometric identities are and why they work.

Lesson Author

Tiffany Dawdy

Phoenix, AZ

Grade Level

Twelfth grade

Subjects

Math

Precalculus and Calculus

Trigonometry

Standards

HSF-TF.C

Prove and apply trigonometric identities.

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.

MP1

Make sense of problems and persevere in solving them.

MP2

Reason abstractly and quantitatively.

MP6

Attend to precision.

MP7

Look for and make use of structure.

Accessing Prior Knowledge

10 minutes

DiscoverTrigID_Dawdy_AccessPriorKnowledgeNarrative.pdf page 1

Investigation

30 minutes

Closure

10 minutes

As a closure to today’s lesson have students complete the fourth page in their trig identities book with the Pythagorean identities. I ran this similar to yesterday’s lesson. I just facilitated a whole class discussion of the findings by having students raise their hands to share their answers. Then I clearly wrote out the Pythagorean identities on the board to ensure all students are copying them correctly (MP6). I personally chose to only have my students list the three standard identities and then I will expect them to be able to manipulate these to obtain the other variations of these (MP7). I know some resources list all the identities solved for each term, but I think the students should be able to do that.

Finally, I had students attempt the last question on the Flipchart (MP1). As in previous lessons this week, this task previews upcoming work. I plan to go over all of these preview questions from the week in tomorrow’s lesson as an introduction to solving basic trig identities.