Question

The function y=sin(t) oscillates between a minimum value of y=−1 and a maximum value of y=1. multiplying this function by a number a changes the minimum and maximum values, increasing the magnitudes if a>1 and decreasing the magnitudes if a<1. part a give the minimum and maximum values of the function y=3sin(t). give the minimum value followed by the maximum value, separated by a comma.

Answer 1

For f(t) = 3 sin(t), the minimum is -3, the maximum is 3.
For additional information:
The period T of the function y=3sin(4t) is;
The period of y = 3 sin (4t) is (2pi) / 4 = pi / 2

The sine function with amplitude A = 0.75 and period T = 10, is
y = 0.75 sin( (2pi / 10) x )
= 0.75 sin( (pi/5) t)
y(4) = 0.75 sin( (pi/5) (4) )
= 0.75 sin ( (4/5) pi ) = .4408

Drawing the sine and cosine function on the same plot shows
that they are identical except for a horizontal shift.
The cosine
function leads the sine function by a shift of (2pi/4) = pi/2.

For the last part, y(4) = 0.75 cos( (2pi/10) (4) ) = - 0.6067