This applet shows dynamic renditions of proofs for the formulas sin(a+b)=sin(a)cos(b)+cos(a)sin(b) andcos(a+b)=cos(a)cos(b)-sin(a)sin(b). The applet can be switched between the two proofs via a radio button.
Type of Material:
Demonstration/Simulation.
Recommended Uses:
This applet would be a useful classroom supplement when discussing these identities.
Technical Requirements:
Should run in any java-enabled browser.
Identify Major Learning Goals:
Ability to reproduce the formulas for sin(a+b) and cos(a+b). Visual exposure to the proofs of these formulas.
Target Student Population:
Students in trigonometry and/or geometry.
Prerequisite Knowledge or Skills:
Angles, the unit circle, and the definitions of the sine and cosine function should be known.
Content Quality
Rating:
Strengths:
This applet gives a depiction of a possible proof of the identity for sin(a+b). In the first quadrant this proof is entirely obvious and very elegant.
Concerns:
If the sum of the angles is larger than 900 the visualization of the proof gets a bit tedious. The use of arrows as directed distances in the applet may require some basic vector knowledge.
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
Very focused applet for quickly demonstrating an elegant proof. The dynamic feature of being able to adjust the angles allows the teacher to demonstrate that the proof forces the equality to be valid independent of what inputs one chooses. This is something that is challenging for some students.
A printout of the unlabeled applet could be turned into an exercise in which students are led to discover the identity by identifying the right lengths in a sketch that involves triangles.
Concerns:
None.
Ease of Use for Both Students and Faculty
Rating:
Strengths:
Extremely easy to use.
Concerns:
Applet only accepts angles up to a size of 1800 for the angle B and 900 for the angle A. The applet page would benefit from adding navigation buttons.
Creative Commons:
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