Question

Find all solutions in the interval [0, 2π).

cos x = sin x

Answer 1

divide both sides with sinx

Answer 2

then i get cos/sin but how do i relate that to interval 0 and 2pi

Answer 3

why would you divide both sides by sin(x)

Answer 4

square both sides :
cos^2 x = sin^2 x
cos^2 x = 1 - cos^2 x
2cos^2 x = 1
2cos^2 x - 1 = 0
(sqrt(2)cosx + 1)(sqrt(2)cosx - 1) = 0
now, set each factor be zero then solve for x

Answer 5

oh thats clever

Answer 6

cotx = 1

tanx = 1

x = pi/4, + ?

Answer 7

your a clever little baby RadEn, I assume thats you in your profile picture

Answer 8

that's my son's pic
heh :)

Answer 9

so pi/4 and 5pi/4? or is it 7pi/4

Answer 10

since tanx period is pi, pi+pi/4 also satisfies the solution

so, x = pi/4, pi+pi/4
= pi/4, 5pi/4

Answer 11

Thank you sara!

Answer 12

yw :)