sin (2x+pi/6) =1/2 core: 0 of 2 pts 5.37 Solve the following equation on the int

Question

sin (2x+pi/6) =1/2 core: 0 of 2 pts 5.37 Solve the following equation on the interval [0.2x) 32 of 40 (31 complete) HW Score: 71 8396, 51 of 71 pts Question Help 6 2 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. x y ear Exact answer in terms o#x Use a comma to separate answers as needed. Use integers or ractions for any numbers in the expression 0 B. There is no solution. + More Click to select and enter your answer(s) and then click Check Answer Clear All All parts showing

Explanation / Answer

sin(2x + pi/6) = 1/2

2x + pi/6 = 2npi + pi/6 , 2npi + 5pi/6

2x + pi/6 = 2n*pi+ pi/6
or
2x + pi/6 = 2n*pi + 5pi/6

Simplifying each :
2x = 2n*pi
2x = 2n*pi + 2pi/3

Divide by 2 :
x = n*pi
x= n*pi + pi/3

We must plug in so that x lies between [0 , 2pi)

So, we can do n = 0 and 1

With n = 0 and 1, we get :
x = 0 , pi , pi/3 , 4pi/3

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