InterMath Exploration

Specific Expectations

2.5 determine, through investigation using technology, the roles of the parameters a, k, d, and c in functions of the form y =af (k(x – d)) + c, where f(x) =sinx or f(x) =cosx with angles expressed in degrees, and describe these roles in terms of transformations on the graphs of f(x) =sinx and f(x) =cosx
2.4 sketch the graphs of f(x) =sinx and f(x) =cosx for angle measures expressed in degrees, and determine and describe their key properties

Materials

Internet, graph paper or a printer, radian to degrees cheat-sheet

Important Terminology

amplitude, period, frequency, phase shift, phase angle,

Background Knowledge

Hook

Lesson Sequence

1. Review the actions of a, k, c, and d on a quadratic function.
2. Review the properties domain, range, intercepts, maximum and minimum values, increasing/decreasing intervals).
3. Have the students predict what effect the parameters a, k, c, and d have on the graph y=a sin(k(x+d)) +c and it's properties and record it in their journals
4. Go over the relationship between radians and degrees
5. Have the students complete sections 1, 2, and 3 from Graphs of the Trigonometric Functions In additions, have them list cycle, domain, range, intercepts, amplitude, period, maximum and minimum values, increasing/decreasing intervals for their graphs.
6. Have the students compare what they've learned with what they predicted.

Key Questions

Leading questions given by you to the students and expected questions from the students

Assessment

Formative - collect the graphs they produce

Enrichment

Those who finish early can work on the remaining sections of the webpage.

Remediation

THere is also an excellent app at GeoGebra that lets you play with all the trasforming variables for any trig function.

Implications for Future Lessons