Here the teacher can remind or teach students that tangent lines touch circles at only one point. Once again the teacher can invoke prior knowledge by asking students what they know about the original triangle and the new triangle just drawn. When students respond they are similar triangles and the conversation develops to emphasize that similar triangles have proportional sides, the teacher can help students form a proportion with the ratio of sine and cosine equal to the ratio of tangent and the radius of the circle. And since the radius of the circle equals 1, the students will have discovered that tangent equals the ratio of sine and cosine. Instead of asking students to memorize the widely-known trigonometric ratio, students will have discovered the ratio intuitively and will have a higher probability of retention in long-term
Here the teacher can remind or teach students that tangent lines touch circles at only one point. Once again the teacher can invoke prior knowledge by asking students what they know about the original triangle and the new triangle just drawn. When students respond they are similar triangles and the conversation develops to emphasize that similar triangles have proportional sides, the teacher can help students form a proportion with the ratio of sine and cosine equal to the ratio of tangent and the radius of the circle. And since the radius of the circle equals 1, the students will have discovered that tangent equals the ratio of sine and cosine. Instead of asking students to memorize the widely-known trigonometric ratio, students will have discovered the ratio intuitively and will have a higher probability of retention in long-term