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Period, Amplitude, Range, Y-intercept and Phase Shift

Develop the solutions for the following problems:

1.) Graph the function y = -1 + 2sin(x + π) over a 2-period interval.
a. What is it's period?
b. What is its amplitude?
c. What is it's range?
d. What is the y-intercept of it's graph?
e. what is it's phase shift?

2.) The formula for the up and down motion of a weight on a spring set in motion is
s(t) = a sin √k/m t

If the spring constant k is 6, what mass m must be used to produce a period of 1 sec.
Hint: period = 2л/w

Solution Preview

a function f is periodic with period t if
f(x + t) = f(x)
for all values of x in the domain of f.

Please see the attached figure..

A. From the graph we can see that the funtion has the same value when x = 2pi, 4pi etc. But the least positive value for which such a ...

Solution Summary

Period, Amplitude, Range, Y-intercept and Phase Shift are calculated for a given trigonometric function. A formula for weighted spring is elucidated. All work is shown.