As teachers, we should amend our way of teaching so we are explaining and analyzing the concepts more deeply. For trigonometry, students will learn better if they are taught how to estimate using the coordinate grid and the unit circle. Understanding that the unit circle has a radius that is 1 unit, will help students estimate. They can look at the x and y components of a given angle based on how close or far it is to 1. This can help students understand/realize that the maximum value of sine and cosine graphs must be 1 and the minimum value must be -1. All other values will be between 1 and -1, which are easily estimable using the unit circle. Below is an image of the unit circle (Figure 1) which students are taught in school but this is just another variation of the special triangles. It does not teach you how to estimate an angle such as sin of 70 degrees.
Usually students are told to use the calculator and asked to round to two decimal places when asked to solve an angle that cannot be solved using special triangles (ex. sin 70). When plugging values into their calculators, students do not truly understand what their answer even means, it is just a number to them. If we start teaching students how to estimate, it will strengthen their understanding. Using the second figure, can see that the angle is being estimated by looking at the lengths of the x and y components of the terminal arm. By first being able to draw the prinicpal angle, create the components, understand how to find sine, cosine, and tangent, we are able to estimate any angle.
![]() ![]() |
No comments:
Post a Comment