At A-Level, trigonometry becomes rather advanced in a short space of time. Are students given enough time to form a solid understanding of radians on which to build? Compare it to degrees, where students learn:
- how to measure angles
- how to estimate angles
- angle facts in triangles and quadrilaterals
- angles in parallel lines
- interior and exterior polygons
- trigonometric ratios, Sine Rule, Cosine Rule and areas of triangles
- trigonometric graphs
- (in year 12) trigonometric equations
I'm not suggesting that students dedicate the same amount of time to radians, as some existing schema will already be in long term memory from working in degrees. I'm suggesting that students get some experience working with radians in these areas to make them less abstract, fully embed new information alongside existing schema and develop a solid foundation to build upon, with the aim of reducing misconceptions on more complicated problems later.
Here is a worksheet where angles are fractions of π in radians and students either use radian protractors or they use regular protractors and convert to radians.
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