Aim: How do we find the sine and cosine ratios in right triangles?

Learning objectives: Students will be able to express the sine and cosine of an angle as a ratio. Students will be able to find missing side lengths for any right triangle.

Prerequisite knowledge: Students should know how to write tangent ratios. Students should know how to solve for a missing leg given the length of the other leg.

Motivational problem: 1. B = 37°, C = 90°, b = 12, a = ? 2. A = 90°, B = 70°, b = 10, c = ?

Key ideas: SOHCAHTOA sine = opposite/hypotenuse, cosine = adjacent/hypotenuse. The hypotenuse is the longest side in a right triangle and is always opposite the right angle. The opposite and adjacent angles depend on the angle being measured.

Important questions: When is the sine ratio the biggest? When is the sine ratio the smallest? When is the cosine ratio the biggest? When is the cosine ratio the smallest? How are the sine, cosine, and tangent ratios related?

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