Question

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 ?

Answer 1

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

Answer 2

solve it

Answer 3

\[\large sinx=cosx\]

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

sin 45 and cos 45

Answer 8

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

Answer 9

oh okay so x = 45.

Answer 10

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

Answer 11

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

Answer 12

45 - 180 = -135
x= -135?

Answer 13

other way.... 180+45

Answer 14

oh 225 ?

Answer 15

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

Answer 16

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

Answer 17

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

Answer 18

okay thanks ! :)

Answer 19

yw...:)

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

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