how would i predict values of x for which the graphs of y=sin(x) and y=cos(x) will intersect in the interval from 0 to 360 degrees ?

do you actually want to solve this or is the question how do you predict the solution?

solve it

\[\large sinx=cosx\]

\[\large \frac {sinx}{cosx}=1 \rightarrow tanx = 1\]

i divided both sides by cosx to get tanx =1.

ok. what values of x will give you a value of 1?

sin 45 and cos 45

you only want the angle x... so x=45 correct?

oh okay so x = 45.

but so fast.... there is another answer.... [HINT: x is in the third quadrant]

the angle in the third quadrant has 45 as its reference angle... :)

45 - 180 = -135 x= -135?

other way.... 180+45

oh 225 ?

yep.... so those are your two solutions between 0 and 360 in which sinx = cosx... good work alexies... :)

thank you ! :) so it i were to look for values from -360 to 360 i'd just subtract from 45 right?

yes... make sure the angles are COTERMINAL with these two angles of 45 and 225 and you'll be fine... :)

okay thanks ! :)

yw...:)

btw.. it's saturday... why homework?

haha yeah, and cause the school year's almost over and i need to get caught up so i don't take summer school. :P

oo... let me know if you need anymore help then! you should be having fun over the summer and not going to school...

oh wow thank you so much ! & yep :) I'm leaving the country right after the last day of exams haha.