Unpacked Content
Knowledge
Students know:
- Methods for finding the sine, cosine, and tangent ratios of a right triangle.
- The Pythagorean Theorem.
- Properties of equality.
- The signs of the sine, cosine, and tangent ratios in each quadrant.
Skills
Students are able to:
- Use the unit circle, definitions of trigonometric functions, and the Pythagorean Theorem to prove the Pythagorean Identity sin2 (θ) + cos2(θ) = 1.
- Accurately use the Pythagorean identity sin2 (θ) + cos2(θ) = 1 to find the sin(θ), cos(θ), or tan(θ) when given the quadrant and one of the values.
Understanding
Students understand that:
- The sine and cosine ratios and Pythagorean Theorem may be used to prove that sin2 (θ) + cos2 (θ) = 1.
- The sine, cosine, or tangent value of an angle and a quadrant location provide sufficient information to find the other trigonometric ratios.
Vocabulary
- Pythagorean Identity
