for the acute angles in a right triangle, sin(2x)=cos (4x+12 degree). what is the measure of the larger angle?
Since the triangle is a right triangle, one of the acute angles is 90 degrees.
Let's assume the other acute angle is x degrees.
According to the given equation, sin(2x) = cos(4x + 12 degrees).
Using the identity sin(2x) = cos(90 degrees - 2x), we can re-write the equation as cos(90 degrees - 2x) = cos(4x + 12 degrees).
Since the cosine function is an even function (cos(-a) = cos(a)), we can set the contents of the cosine function equal to each other:
90 degrees - 2x = 4x + 12 degrees.
Simplifying the equation:
90 - 12 = 4x + 2x,
78 = 6x,
x = 13.
Therefore, the measure of the larger angle is 90 - 2x = 90 - 2 * 13 = 90 - 26 = 64 degrees.