Tasks | Early Adolescence | Investigating the Sine & Cosine Curves

Tasks - Years 10, 11 & 12

Investigating the Sine & Cosine Curves   by Thelma Perso, Senior Curriculum Officer Mathematics

Phase of Development:   Early Adolescence - Late Adolescence

Learning Area/s:	Mathematics
Strand/s	Substrand/s
Algebra	Understand Graphs Represent Variation Understand Symbols
Measurement	Understand Units
Working Mathematically	Apply and Verify Mathematical Strategies
Expected Outcomes:	Students understand the relationship between degrees and radians. Students understand the graphic relationship between the sine and cosine curves.
Context:	Year 10, Foundations of Mathematics. I have used this task with year 10 and 11 students.
Learning Activities/ Experience:	Students use their graphics calculator to make decisions about relationships between the sine and cosine curves and between the units of measurement: degrees and radians.
Resources:	Graphics Calculators Worksheet

Worksheet

Investigating the Sine & Cosine Curves

Put your calculator into Trig (for graphing) and draw the graph of y = sine x (adjust the scale and max/min values so that the graph is large enough).

Using the TRACE button, write down the degrees (x) and then the Y value (Sine x) in each case. Once you have done that change the MODE to Radians and write the Radian (x) measure down in each case as well as the Y value (Sine x).

Deg (x)	0
y = Sin x	0
Rad (x)	0
y = Sin x	0

Do you get the same sine values? __________________________________________________

Use the formula to change degree values to the equivalent radian values to confirm this. Now repeat the above work for the Cosine graph. Draw the graph and complete the table.

Deg (x)	0
y = Cos x	0
Rad (x)	0
y = Cos x	0

Do you notice anything about the values in the two tables? Write about what you notice.