The functions sine and cosine from 0 to 360 degrees

A complete lesson on the graphs of sine and cosine from 0 to 360 degrees. I’ve also made complete lessons on tangent from 0 to 360 degrees and all three functions outside the range 0 to 360 degrees.

Designed to come after pupils have been taught about the ratios sine, cosine and tangent in the context of right-angled triangle trigonometry.

Activities included:

Starter:
Examples to remind pupils how to find unknown angles in a right-angled triangle (see cover slide), followed by two sets of questions; the first using sine the second using cosine. The intention is that pupils estimate using the graphs of sine and cosine rather than with calculators, to refamiliarise them with the graphs from 0 to 90 degrees. Although I’ve called this a starter, this part is key and would take a decent amount of time. I would print off the question sets and accompanying graphs as a 2-on-1 double sided worksheet.

Main:

• Slide to define sine and cosine using the unit circle, with a hyperlink to a nice geogebra to show the graphs dynamically. Or you could get pupils to try to construct the graphs themselves by visualising.
• A set of related questions that I would do using mini-whiteboards, where pupils consider symmetry properties of the graphs.
• A mini-investigation where pupils look at angles with the same sine or cosine and look for a pattern.

Plenary:
An image to prompt discussion about the “usual” definition of sine and cosine (using the terminology opposite, adjacent and hypotenuse) and the fuller definition (using the unit circle)

Printable worksheets and answers included.

Please review if you buy as any feedback is appreciated!