what is the solution set for sin x cos x = square root of 3/4?
`sinxcosx = sqrt(3)/4`
To solve, apply the double angle identity `sin(2theta) = 2sinthetacostheta` .
`(sin (2x))/2 =sqrt(3)/4`
Then, multiply both sides by 2 to have sin(2x) only at the left side.
In the Unit Circle Chart, sine function has a value of sqrt3/2 at angles pi/3 and 2pi/3. Since it is a double angle, add each of these two angles by 2pi. So the values of angle 2x are:
`2x = pi/3 , (2pi)/3, (7pi)/3, (8pi)/3`
Then, isolate the x.
`x = pi/6, pi/3, (7pi)/6, (4pi)/3`
Moreover, there is no given interval for x. So the solution is in general form. To express this in general form, notice that the difference between pi/6 and 7pi/6 is pi. And the difference between pi/3 and 4pi/3 is pi.
Thus, the solution are: