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Algebra 2/Trig Name: 10.02 Solving Quadratic Trig Equations Aim: I can solve quadratic trigonometric equations Mildly Spicy 1. Determine all solutions for all rotations between to 360°. Use the hand rule. a. sin = ! ! b. cos = 1 c. cos = ! ! Spicy 2. Determine all solutions for all rotations between to 360° a. 2 () 1 = 0 b. 2cos () 1 = 0 Spicier 2. Determine all solutions for all rotations between to 360° a. 2 ! () 1 = 0 b. 2 sin ! sin = 1 c. 2 cos ! + cos + 2 = 3 d. 3 cos ! + 14 cos + 8 = 0

Transcript of 10.02 Quadratic Trig Equations - WordPress.com · Algebra 2/Trig Name: 10.02 Solving Quadratic Trig...

Algebra2/Trig Name:10.02 Solving Quadratic Trig Equations Aim: I can solve quadratic trigonometric equations Mildly Spicy 1. Determine all solutions for all rotations between 0° to 360°. Use the hand rule.

a. sin 𝜃 = !! b. cos 𝜃 = 1 c. cos 𝜃 = !

!

Spicy 2. Determine all solutions for all rotations between 0° to 360° a. 2 𝑠𝑖𝑛(𝜃)− 1 = 0 b. 2cos (𝜃)− 1 = 0 Spicier 2. Determine all solutions for all rotations between 0° to 360° a. 2 𝑠𝑖𝑛!(𝜃)− 1 = 0 b. 2 sin! 𝜃 − sin 𝜃 = 1 c. 2 cos! 𝜃 + cos 𝜃 + 2 = 3 d. 3 cos! 𝜃 + 14 cos 𝜃 + 8 = 0

Algebra2/Trig Name:Cinnamon Challenge Spicy 3. Determine all solutions for all rotations between 0° to 360° a. tan! 𝜃 − 3 tan 𝜃 + 2 = 0 b. 4𝑠𝑖𝑛𝜃 + 7 = 3 c. To the nearest tenth of a degree, find all values of 𝜃 in the interval 0° ≤ 𝜃 < 360° 6cos! 𝜃 − 5 sin 𝜃 − 5 = 0 1 **Finished: Try These! ** #Throwback! 4. Solve: −10+ 2 −9− 2𝑘 = −8 5. Solve: 5𝑝! − 8𝑝 + 6 = 0

d. Writing in Math! Is tan!(𝜃) the same thing as tan(𝜃)!? Explain why or why not. What does each mean?

e. In order for 2𝑥! + 7𝑥 + 5 = 0 to be true, you have to solve for x values that make the equation true/work. Using that logic, in order for tan!(𝜃)−3 tan(𝜃)− 4 = 0 to work, what values must we look for that satisfies the equation!