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Inspecting Identities

Age 16 to 18 Challenge Level:

This resource is from Underground Mathematics.


Take a look at these identities.

$$ \cos^2 \frac{\theta}{2} \equiv \frac{1}{2}(1+\cos \theta) \quad \quad \quad \sin^2 \frac{\theta}{2} \equiv \frac{1}{2}(1-\cos \theta)$$

How could you use these identities to help you sketch graphs of $y=\cos^2 \frac{\theta}{2}$ and $y=\sin^2 \frac{\theta}{2}$?




This is an Underground Mathematics resource.

Underground Mathematics is funded by a grant from the UK Department for Education and provides free web-based resources that support the teaching and learning of post-16 mathematics. It started in 2012 as the Cambridge Mathematics Education Project (CMEP).

Visit the site at to find more resources, which also offer suggestions, solutions and teacher notes to help with their use in the classroom.