Draw a triangle with angles x, (45 + x) and (45 – x) degrees.

What does Pythagoras Theorem tell you about these angles?

Use this information to find this sum of squares of sines:

\sin^2 1 + \sin^2 2 + \cdots + \sin^2 359 + \sin^2 360


Click here to download the DEGREE CEREMONY worksheet.

See the AIMSSEC Notes for Teachers.

This problem is adapted from the NRICH task Degree Ceremony with permission of the University of Cambridge. All rights reserved.

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