Question

Find all solutions to the equation.

cos x = sin x

Answer 1

Hint:

\[\cos(x) = \sin(x)
\\\frac{\sin(x)}{\cos(x)} = 1
\\\tan(x) = 1
\]

Answer 2

How does sin x/cos x equal to 1?

Answer 3

nvm, i see it

Answer 4

Good

Answer 5

so sin x and cos x are both (sqrt. 2)/2 ? pi/4?

Answer 6

Yes. The reason is because of the co-function rule
sin(x) = cos(y) whenever x + y = 90

Answer 7

In this case, x = y = pi/4

Answer 8

Well, actually, that's just one of the solutions. You'll have to add 180 everytime to get all the solutions. So pi/4 + k*pi