Question 1125522
let y = f(x).


equation becomes y = 4 * sin^2(x) - 3


set y = 0 and the equation becomes 4 * sin^2(x) - 3 = 0


divide both sides of the equation by 4 to get sin^2(x) - 3/4 = 0


add 3/4 to both sides of the equaton to get sin^2(x) = 3/4


take the square root of both sides of the equation to get sin(x) = plus or minus sqrt(3/4) which is equal to sqrt(3) / sqrt(4) which is equal to sqrt(3) / 2.


you get sin(x) = plus or minus sqrt(3)/2.


you can use your calculator to solve for x, or you can remember that arcsin(sqrt(3)/2) = 60 degrees.


60 degrees * pi / 180 = pi/3 radians.


that's your angle in the first quadrant in radians.


in the second quadrant, the angle is pi - pi/3 = 2/3 * pi = 2pi/3.


in the third quadrant, the angle is pi + pi/3 = 3pi/3 + pi/3 = 4pi/3.


in the fourth quadrant, the angle is 2pi - pi/3 = 6pi/3 - pi/3 = 5pi/3.


since arcsin is plus or minus, then all 4 quadrants apply and you solution is:


x = pi/3, 2pi/3, 4pi/3, 5pi/3 in the interval [0,2pi].


in degrees, that would be x = 60, 120, 240, 300 in the interval [0,360].


i graphed the equation of y = 4 * sin^2(x) - 3 in degrees and radians in the interval [0,360] and [0,2pi].


the graphs are shown below:


<img src = "http://theo.x10hosting.com/2018/100801.jpg" alt="$$$" >


<img src = "http://theo.x10hosting.com/2018/100802.jpg" alt="$$$" >


the graph confirms that y = 4 * sin^2(x) - 3 = 0 at those values of x.