Cavalieri Research Paper

The cosine was developed as the sine of the complement of the angle, and notation for cosine was also varied. The term sinus residuae was used by Viete while Gunter preferred co-sinus in the year 1620. Cavalieri used Si.2, Oughtred used s co arc and Wallis used S [2]. The tangent and cotangent developed out of the need to calculate the height of an object casting a shadow of a certain length, which was of critical importance for the sundial. Thales is known to have used the method of lengths of shadows to estimate the height of the pyramids [2]. The method turned into the development of the tables of shadows, and the Arabs produced the first tables around 860 translated later with the terms umbra recta and umbra versa. Viete referred to them as am sinus and pro sinus, and Thomas Fincke first used the term tangent in 1583 while Edmund Gunter first used the term cotangent in 1620. Cavalieri utilized Ta …show more content…
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