Question

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

cos x = sin x

Answer 1

pi/4

Answer 2

just use tan x= 1 and solve for x

Answer 3

x has to be pi on 4 for both to be equal

Answer 4

pi/4 and 7pi/4 right?

Answer 5

u cant have 7pi on 4

Answer 6

cause the 4th quadrant is positive for cos values but negative for sin values

Answer 7

5pi/4

Answer 8

ucant...

Answer 9

ou can rewrite sin2x using the double angle formula to get:

cosx = 2*sinx*cosx... subtract cosx on both sides
2sinxcosx - cosx = 0... factor
cosx(2sinx - 1) = 0

Set each factor equal to zero to get two sets of roots:
cosx = 0 ==>
x = {π/2,3π/2}
2sinx - 1 = 0 ==> sinx = 1/2 ==>
x = {π/6, 5π/6}

Answer 10

ur interval is form 0 < x < 2pi

Answer 11

the only x values that is common to both cos x = sin x is when x = pi/4

Answer 12

YEAH

Answer 13

3pi/4, 5pi/4

pi/4,7pi/4

3pi/4, 7pi/2

pi/4, 5pi/4