MA19.A2.36

Mathematics (2019) Grade(s): 09-12 - Algebra II with Statistics

MA19.A2.36
Prove the Pythagorean identity $\sin^2 (\theta) + \cos^2 (\theta) = 1$ and use it to calculate trigonometric ratios.

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

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