cos(3x - Pi/4) = 0?

Question

Find the solutions of the equation that are in the interval [0, 2*Pi); separate your answer

Answer 1

we know that the zeros of cos occur at -3Pi/2, -Pi/2, Pi/2, 3Pi/2 ...
more generally (2k+1)Pi/2 for all k integers
(k=..., -4,-3,-2,-1,0,1,2,3,4....)

So we want to solve 3x-Pi/4 = (2k+1)Pi/2

simplify to give x = (4k + 3)Pi/4

Now choose the values of k that give x in the interval [0,2Pi).

Answer 2

cos(3x - (pi/4)) = 0
cos((12x - pi)/4) = 0

cos^-1 both sides

(12x - pi)/4 = (pi/2) or ((3pi)/2)

multiply both sides by 4

12x - pi = 2pi or 6pi

add pi to both sides

12x = 3pi or 7pi

divide both sides by 12

x = (pi/4) or ((7pi)/12)

Answer 3

3x-Pi/4=Pi/2, 3Pi/2, 5Pi/2, etc
3x=3Pi/4, 7Pi/4
x=Pi/4, 7Pi/12