state the amplitude, period, and phase shift of the function -0.4 sin (10x+pie/2)

If you have a function

y = a*sin(k(x-c))

then the
amplitude = |a|
period is 2π/|k|
phase shift is c

so, rewriting your function

y = -.4sin(10(x+π/20))

now just read off the amplitude, period, and phase shift.

To determine the amplitude, period, and phase shift of the function -0.4 sin(10x+π/2), we can analyze different parts of the given equation.

1. Amplitude: The amplitude of a sine or cosine function is the absolute value of the coefficient in front of the trigonometric function. In this case, the coefficient is -0.4, so the amplitude is 0.4.

2. Period: The period of a sine or cosine function is calculated by dividing 2π by the coefficient inside the function, without considering any added constant. The coefficient in this case is 10, so the period is 2π/10, which simplifies to π/5.

3. Phase Shift: To determine the phase shift, we look at the argument of the trigonometric function – the part inside the parentheses. In this function, the argument is 10x+π/2. To find the phase shift, we solve the equation 10x + π/2 = 0 and isolate x. Subtracting π/2 from both sides gives us 10x = -π/2, and then dividing by 10 results in x = -π/20. The opposite sign of -π/20 tells us that the phase shift is to the right by π/20.

Therefore, the amplitude is 0.4, the period is π/5, and the phase shift is π/20.