Question

Trig equations help: Find all solutions in the interval [0, 2π).
cos x = sin x
Really in need of help with this concept so if anyone can explain it to me it would be very appreciated.

Answer 1

look on the unit circle to see where the first and second coordinates are the same
you got a unit circle cheat sheet?

Answer 2

cosine is the first coordinate, sine is the second
there are two points on the unit circle where the first and second coordinates are the same
it is on the last page1

Answer 3

Okay one second I'm looking at it now.

Answer 4

I'm not really sure which two points on the circle have the same first and second coordinates. Each quadrant make a different coordinate negative/positive so isn't that impossible?

Answer 5

hint: look in quadrant 1 and quadrant 3

Answer 6

Is it pi/4 and 5pi/4? I feel like it's really obvious but I'm just not seeing it.

Answer 7

yep

Answer 8

Would that be the final answer then?

Answer 9

you just said them both: pi/4 and 5pi/4

Answer 10

cos(pi/4) = sqrt(2)/2
sin(pi/4) = sqrt(2)/2

this is shown at the point in Q1 with both coordinates equal to sqrt(2)/2

Answer 11

cos(5pi/4) = -sqrt(2)/2
sin(5pi/4) = -sqrt(2)/2

this is shown at the point in Q3 with both coordinates equal to -sqrt(2)/2

Answer 12

Oh okay, thank you so much!

Answer 13

I guess another way to do it is to square both sides and use an identity


sin(x) = cos(x)
sin^2(x) = cos^2(x)
sin^2(x) = 1-sin^2(x)
sin^2(x)+sin^2(x) = 1
2*sin^2(x) = 1


keep going to solve for x


You'll have to check the possible solutions (some possible solutions will be extraneous)

Answer 14

no problem

Answer 15

That makes a lot of sense too, thank you!