Find the falling and rising intervals of a trigonometry function

Question:

Find the monotonic falling and rising intervals of the function y = 3 sin (pi/3 - 2x).

Solution:

Convert the given equation into a standard form. So, y = 3 sin (pi/3 - 2x) = 3 sin [- (2x - pi/3)] = - 3 sin (2x - pi/3). Let 2x - pi/3 = t, then y = -3 sin t.

Draw the graph of y = -3 sin t, we find when t change from - pi/2 to pi/2, the graph of y = -3 sin(t) is monotonic falling. When t change from pi/2 to 3pi/2, the graph of y = -3 sin t is monotonic rising.

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