Question

find the domain and range of (sin x + cos x)

Answer 1

how

Answer 2

What is the range of each function?

Answer 3

-1 to +1

Answer 4

now ?

Answer 5

now satellite73 will help you

Answer 6

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

Answer 7

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

Answer 8

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"

Answer 9

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

Answer 10

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 \(\sqrt{2}\)

Answer 11

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

Answer 12

Guru JEE thanks