Help Please number 13.

http://prnt.sc/avolwe

Question

Help Please number 13. 

http://prnt.sc/avolwe

anthonyym · Answer

You can graph it on a graphing calculator to see

marcelie · Answer

hmm i did but i dont get it

anonymous · Answer

Put your finger on the graph and start going right. If it is going down, it is decreasing. Simply state from where to where it is decreasing

marcelie · Answer

oh okay but how would you solve it though ?

phi · Answer

is this calculus ?

marcelie · Answer

yes

phi · Answer

For Q13, I would take the derivative (as the first step)
can you do that ?

marcelie · Answer

|dw:1461440515598:dw|

phi · Answer

let's look for when the original function is increasing.  that means when its slope is positive.
cos x - sin x > 0
or, because that looks like a pain to evaluate, add sin x to both sides and examine

cox x > sin x

if that happens the original function is increasing.
let's look at cos x and sin x
see the attached

phi · Answer

you can see the cos is bigger than the sin from 0 up to pi/4 (45 degrees)
during that interval the original function is increasing.
then it decreases for a while  any idea on the interval?

then it increases.

marcelie · Answer

hmmm

marcelie · Answer

cant seem to see it .. thats where i have trouble

phi · Answer

what don't you see?

do you understand the "slope" of the original is
cos x - sin x 
?