Question

4=2cos(pi/6t-2pi/3)+4
How do i solve this step by step ith justification for each step? super frustratd thankyou

Answer 1

Assuming there is no typo in the question, we have to solve:

4=2cos(pi/6t-2pi/3)+4

the 4 on each side cancel out, so the equation becomes:

2cos(pi/6t-2pi/3) = 0

Divide by 2 on each side to get:

cos(pi/6t-2pi/3) = 0

cos(x)=0 when x=(k+1/2)π, k∈Z
(i.e. k is an integer).

Therefore we get:

(π/6)t-2π/3=(k+1/2)π

Divide by π on both sides and solve for t:

t/6-2/3=(k+1)/2
t/6 = k/2 + 1/2 + 2/3
t/6 = k/2 + 7/6

Multiply both sides by 6:

t = 3k + 7 where k∈Z