Sarah Stanic Technology Review
Discovering Sine, Cosine, and Tangent in Right Triangle
Technology Description
This applet is targeted for students ages 11-14 or those who have just begun their exploration into trigonometric functions. This applet allows students to manipulate the angle measure of a right triangle to define the three basic trigonometric functions; sine, cosine, and tangent. Students are prompted to figure out how these three functions are defined before actually knowing the definitions of the functions. Students will achieve this by moving the green slider to adjust the angle measure while the two side lengths of the right triangle adjusts accordingly, the hypotenuse remains at 10. As the slider moves, the values for the three functions change as well. Students are prompted to use a calculator to help record their observations of how these three functions are related to the sides of the triangle. Furthermore, students are able to move point D at the bottom of the applet to change the lengths of the sides of the triangle, leaving the angle measure fixed, to demonstrate how these three ratios are independent of the triangles size. This applet is used to help students develop their own definitions of the three basic trigonometric functions without previously knowing the mnemonic device SOHCAHTOA.
How the applet works
When you first go to the website the angle is set at 70 degrees and students are prompted to explore the applet, by changing the angle measure, and to use a calculator to try and figure out how the trigonometric functions are defined. The students are then prompted to move point D to change the size of the triangle and determine if the three trigonometric functions are dependent on the sides a, b, and c and the size of the triangle. At the bottom of the applet students are asked to write out rules for finding sine, cosine, and tangent of any acute angle in a right triangle and to include a diagram explaining their rules.