You can put this solution on YOUR website! equation is 9 * sin(2x) - 28 * cos(2x) = 0
add 28 * cos(2x) to both sides of the equation to get:
9 * sin(2x) = 28 * cos(2x)
divide both sides of the equation by 28 * cos(2x) to get:
9 * sin(2x) / 28 * cos(2x) = 1
since sin/cos = tan, you get:
9 / 28 * tan(2x) = 1
multiply both sides of the equation by 28/9 to get:
tan(2x) = 28/9
solve for 2x to get:
2x = 72.18111109 degrees.
replace 2x in the original equation to get:
9 * sin(72.18111109) - 28 * cos(72.18111109) = 0
evaluate using your calculator to get:
0 = 0, confirming the value of 2x is good.
divide 2x by 2 to get:
x = 36.09055554 degrees.
that's your angle.
graphically, this will look like this:
your solution will be when 2x = 72.181111 degrees and when 2x = 252.181111 degrees.
that means that x = 36.091 degrees or 126.091 degrees.
when x is 36.0191, both sin and cos are positive.
when x is 126.091, both sin and cos are negative.
you were asked to find the value of x between 0 and 90 degrees.
that would be x = 36.091 degrees.
note that, when x = 36.091, y = 9 * sin (2 * 36.091) = 9 * sin(72.181).
values displayed on the graph are rounded to 3 decimal places.
