Degree Ceremony
Why do this
problem?
This problem focuses on the key properties of the sine function
including the basic definition and the periodicity of the
function.
Possible approach
When first introducing sine and cosine for angles less than 90
degrees the best definition is that sine and cosine are the lengths
of the sides of the right angled triangle with hypotenuse 1 unit.
Here use this definition and immediately you can use Pythagoras
theorem to get the sum of the squares of two sines.
Key
question
What can you say about the angles (45 + x) degrees and (45 - x)
degrees, the sines of these angles and the squares of the sines of
these angles?