Explore the ratios to develop the concept of the trigonometric functions.

• Students will identify the effects of changing the sides and angles on the sine, cosine, and tangent ratios.
• Students will apply the properties of similar triangles to develop the definitions of trigonometric ratios in right triangles.
• Students will connect the terms sine, cosine, and tangent with appropriate ratios in a right triangle.
• Students will construct arguments and defend their reasoning with mathematical examples and counterexamples.

• sine
• cosine
• tangent
• adjacent leg
• opposite leg
• hypotenuse
• similar right triangles

This lesson involves manipulating the angles and sides of a right triangle. As a result, students will:

• Observe the conditions under which the ratio does not change.
• Define the trigonometric ratios of sine, cosine, and tangent.