Solve the equation sin (x) cos (x) = 1/4 on the interval [0, 2π).?
I got pi/12 and 13pi/12. It's wrong. can someone help me out with this?
I multiplied the equation by 2, which made the equation sin(2x)=1/2. Then I used the arc sign on the (1/2). so i got 2x=pi/6 which means x=pi/12 and since the interval encompasses the entire circle, the other answer should be 13pi/12, right?
I know I'm wrong, I just want to prove that I need help and that I'm not trying to cheat or pick off free answers.
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2x = π / 6 , 13π/6 , 5π / 6 ,17 π/6
You're on the right track
sin(2x)=1/2
As you say at
2x = π/6 + 2kπ
dividing by 2 gives
x = π/12 + kπ
x = π/12, 13π/12 (both which are part of your answers)
as well as
2x = 5π/6 + 2kπ
dividing by 2 gives
x = 5π/12 + kπ
x = 5π/12, 17π/12 (two additional answers)
The range of the arc sine function is only from -π/2 < x < π/2
You need to figure out the other ones based on the unit circle to meet your given domain of [0, 2π), in this case 5π/6 + 2kπ.