This worksheet assesses learning with respect to the Periodic, Odd, Even and Translation properties of trigonometric functions. These are not demonstrated in the worksheet but are listed at the beginning along with some exact values (e.g. cos(30°)=√3/2, cos(60°)=1/2, etc) which are used in the exercises, of which there are fifteen. Five fully-worked examples are included to show how the symmetry properties are used. Students will need a knowledge of reciprocal functions (csc, sec, cot) as the last couple of exercises are based on those functions. An answer sheet is provided at the end of the worksheet. The more complex exercises are fully worked to show how the answers are arrived at.
I've also created some graph data files which can be used to visually demonstrate the symmetry properties but, unfortunately, the file type is not supported on here so I couldn't upload them. The software to run these files is called Graph and is open source. It's a native Windows application but can be ran on an Apple Mac using Wine. I've used the software for years and is adware and virus free. The cover image for this resource was created directly from Graph. If you would like me to send you the data files then email me at firstname.lastname@example.org. The Graph software can be found at http://www.padowan.dk/
Word and PDF versions of the worksheet provided.