## anonymous 5 years ago what is the maximum value of sinx+cosx where x is any real number??

1. anonymous

it has to be 2, the max val for sin and the max val for cos are both 1. The sum of those is 2. Neitehr function will get any bigger than 1 going to infinity.

2. divanshu

3. anonymous

true they do not equal 1 at the same value

4. divanshu

good ebbflo

5. divanshu

6. anonymous

ok. can you explain the process please??

7. anonymous

the max value is $\sqrt{2}$

8. anonymous

that's right, they don't equal the same thing at the same values,

9. anonymous

the pi over 4 values are the only ones that will give you teh max sum, because they are the same for sin and cos.My mistake.

10. anonymous

Is this for calculus?

11. anonymous

Let $f(x)=\sin x+\cos x$

12. anonymous

no this is for trig

13. anonymous

Then $f^\prime(x)=\cos x-\sin x$

14. anonymous

okay ,sorry

15. anonymous

okay then you reason that $x=\frac{\pi}{4}$ is the value when cosine and sine functions are equal and positive

16. anonymous

okay then you reason that $x=\frac{\pi}{4}$ is the value when cosine and sine functions are equal and positive