Experiences

Searching for values of goniometric functions

Zuzana Kuppeová

Slovakia

High Secondary School

Maths

Teaching in class

Direct

Goniometric functions, their graphs and properties is a topic with which students usually have big problems, so I decided to inform them with my own experience with previous students. The students knew functions sin, cos, tan, cotg already from the elementary school. However they knew their definitions only in the case of the right sided triangle. The aim of the couple of following classes was to teach them the unit circle as well as teaching them to assign values of angles of the unit circle with the values of the goniometric functions and outline their graphs. Reading from this the basic features of the functions was also a part of the class goal.
I have prepared for the students a worksheet on which was drawn a unit circle with a radius of 1 dm placed in a Cartesian coordinate system. First, we addressed the sinus function. We repeated the definition then I outlined on the blackboard a unit circle and students derived what the value of sinus for the outlined angle will look like.
Then the students outlined angles to their own unit circle worksheet using a protractor and the measured values of this function for different angles, which I outsourced for them. We put down these values to the result table. I was delighted when students began shouting measured values and compared their own results with each other. They tried to be as accurate as possible. They hesitated, when the angle was greater than 90° and the values began to repeat, but they found an explanation to this situation. Another problem occurred for an angle greater than 180°. Again, the values began to repeat and after finding answers to my questions they have found that the function will produce negative values. Since each student was making his or her own drawing, now they have a better idea of how they got the values. It was also much easier to sketch a graph of the functions and determine their properties. The same procedures were repeated in the next classes for the other three functions. Progress of work has already been faster. Some students which do not like or are not good at sketching and drawing graphs did not like such a lesson. Compared with previous years, I felt that students better understood the curriculum and also earned higher grades at the written test exams.