Question

this value of y is a of​ t(y). because is for all values of​ y, it follows that the value of y found in the previous step corresponds to a local minimum of​ t(y).

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

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