Sum of square sin() functions

[Aikon]

Hi all,
I work as monitor for a pre-university course and one student showed me this problem:

1. The problem statement, all variables and given/known data
To find how much is y:
y=sin2(10)+sin2(20)+sin2(30)+...+sin2(80)+sin2(90)

2. Relevant equations
I don't know. I thought about sen2x+cos2x=1


3. The attempt at a solution
To use the equation given above and to write a series of cos()'s, but i don't think it get better than before.

[ehild]

2. Relevant equations
I thought about sin2x+cos2x=1


You are on the right track. Use also that sin(x)=cos(90-x). For example, sin(80°)=cos(10°).

ehild

[Mark44]

There's another identity that I think will be helpful:
sin^2(x) = \frac{1 - cos(2x)}{2}

Also, cos(x) = -cos(\pi - x)

[Aikon]

Thank you all the answers.

I liked this:
You are on the right track. Use also that sin(x)=cos(90-x). For example, sin(80°)=cos(10°).

ehild

With this identity it becomes almost trivial, because (sin210 +sin280)=1 and it goes like this for other pairs, it gives 5 in the end.