## soty2013 3 years ago find the domain and range of (sin x + cos x)

1. soty2013

how

2. math>philosophy

What is the range of each function?

3. soty2013

-1 to +1

4. soty2013

now ?

5. math>philosophy

6. satellite73

it might help to know that $$a\sin(x)+b\cos(x)=\sqrt{a^2+b^2}\sin(x+\theta)$$ for suitable $$\theta$$ that should help a great deal with the range

7. soty2013

asin(x)+bcos(x)=a2+b2−−−−−−√sin(x+θ) but how do you get this ?

8. satellite73

square root is on the outside it is $$\sqrt{a^2+b^2}\sin(x+\theta)$$ and it is a consequence of the "addition angle formula"

9. soty2013

@satellite73 i am having very problem in it... can you explain the function chapter from the starting, i will be very thankful to you..

10. satellite73

i do not know exactly what you mean by "explain the function chapter" you could graph the function $\sin(x)+\cos(x)$ using technology to see what you get or you could surmise that the largest the sum could be is if they were the same value, making $$\sin(x)=\frac{\sqrt{2}}{2}$$ and also $$\cos(x)=\frac{\sqrt{2}}{2}$$ and therefore the max would be $$\sqrt{2}$$

11. satellite73

or more simply you could use the formula i wrote above, telling you that $\sin(x)+\cos(x)=\sqrt{2}\sin(x+\frac{\pi}{4})$ and now the range is more or less obvious

12. soty2013

Guru JEE thanks