Question

PLEASE HELP!! THANK YOU!

Which of the following are solutions to the equation sinxcosx = 1/4?
Check all that apply
A. 5(pi)/12 +n(pi)
B. pi/3 + n(pi)/2
C.pi/12 + n(pi)
D. pi/6 + n(pi)/2

i think it might be A , C and possibly D but I'm not sure... please help I've been struggling with this for the past hour and a half

Answer 1

Recall that 2sinxcosx = sin2x.
Thus, sinxcosx = sin2x/2

So,
`(sin2x)/(2) = (1)/(4)`

`sin2x = (1)/(2)`

`2x = (\pi)/(6), (5\pi)/(6)`

`x = (\pi)/(12), (5\pi)/(12)`

In general form:

`x = \pi n + (\pi)/(12)`

`x = \pi n + (5\pi)/(12)`

Answer 2

Answers A and C and correct for this equation.