Find the amplitude, period, and phase shift of y=5csc(pix-pi)
since the range of csc(x) is (-∞,∞) there is no value for the amplitude.
You are correct. I apologize for my previous mistake. The amplitude for the csc function is not defined because the range of the csc function is (-∞,∞). Therefore, there is no amplitude for the function y = 5csc(pix - pi).
The period of the function can still be determined, which is 2 because it is derived from the period of the trigonometric function.
The phase shift of the function is pi because it is determined by the value inside the parentheses of the function, which is pix - pi. When x = 0, the argument becomes -pi, resulting in a phase shift of pi units to the right.
To summarize, the period of the function is 2 and the phase shift is pi.
To find the amplitude, period, and phase shift of the function y = 5csc(pix - pi), we need to compare it to the standard form of the csc function: y = A csc(Bx - C) + D.
The amplitude of the csc function is the absolute value of A, so in this case, the amplitude is |5| = 5.
The period of the csc function is given by 2π/B. In this case, the coefficient of x is pi, so B = pi. Therefore, the period is 2π/pi = 2pi/pi = 2.
The phase shift of the csc function is C/B. In this case, the constant term is -pi, so C = pi. Therefore, the phase shift is pi/pi = 1.
So, the amplitude is 5, the period is 2, and the phase shift is 1.