Sketch a triangle with angles $90^\circ$, $(45+x)^\circ$ and $(45-x)^\circ$.

Use your diagram, and Pythagoras' Theorem, to help you find the sum:  $$ \sin^2 1^\circ + \sin^2 2^\circ + \, \cdots \,+ \sin^2 89 ^\circ + \sin^2 90^\circ$$

 

 

Find also: $$ \sin^2 1^\circ + \sin^2 2^\circ + \, \cdots \,+ \sin^2 359 ^\circ + \sin^2 360^\circ$$