# Thread: 【TRIGONOMETRY】help with one quiestion?

1. ## 【TRIGONOMETRY】help with one quiestion?

Question: If sin x + sin y =1 , what is the range of values of cos x + cos y?

Thanks!

2. ## Re: 【TRIGONOMETRY】help with one quiestion?

He HeilKing.

Hint: Try using cos(x) = sin(x+pi/2) and simplifying.

3. ## Re: 【TRIGONOMETRY】help with one quiestion?

Hey King
This is a very tricky question . I am publishing a solution that is based on a lemma as discribed below.
If anyone needs a proof of this lemma he has to sent me an e-mail.

Attachment 28620

4. ## Re: 【TRIGONOMETRY】help with one quiestion?

Hi Heilking,
I don't think Minoanman's answer is what you want. His inequality is not sharp. Here's what I think you want. Let the curve C have equation sin(x)+sin(y)=1. Then the set of values (range) {cos(x)+cos(y) : (x,y) is a point on C} = $\displaystyle [-\sqrt3,\sqrt3]$
The first attachment shows the graph of C. From this graph (and analytically), you can see that the range can be found by considering only values of x and y in [0,pi].

The second attachment shows the graph for C represented parametrically. From this representation, one can find the range. If you have any questions, just respond to this post.