Answer:To find the zeros of the basic cycle of the graph of y = 3 sin (5x + 60°) between 0° and 360°, we need to determine the values of x that make y equal to zero.
The zeros of a sine function occur when the value of sin is equal to zero. In the basic cycle, the sine function reaches zero at regular intervals.
To find the zeros of the given function, we can set 3 sin (5x + 60°) equal to zero and solve for x.
0 = 3 sin (5x + 60°)
To find the values of x, we need to find the angles whose sine is zero. The angles that satisfy this condition are multiples of 180°.
Setting 5x + 60° equal to 180°, we can solve for x:
5x + 60° = 180°
5x = 180° - 60°
5x = 120°
x = 120°/5
x = 24°
Therefore, one zero of the basic cycle is x = 24°.
Similarly, we can find the other zeros by adding multiples of 180° to the initial value of x:
x = 24° + 180° = 204°
x = 24° + 2(180°) = 384°
Therefore, the zeros of the basic cycle of the graph of y = 3 sin (5x + 60°) between 0° and 360° are x = 24°, x = 204°, and x = 384°.