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 ?

Question

anonymous · Answer

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

anonymous · Answer

solve it

anonymous · Answer

$$\large sinx=cosx$$

anonymous · Answer

$$\large \frac {sinx}{cosx}=1 \rightarrow tanx = 1$$

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

sin 45 and cos 45

anonymous · Answer

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

anonymous · Answer

oh okay so x = 45.

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

45 - 180 = -135
x= -135?

anonymous · Answer

other way.... 180+45

anonymous · Answer

oh 225 ?

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

okay thanks ! :)

anonymous · Answer

yw...:)

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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