SOLUTION: Given the curve y=sin(1/2thetha-90 degrees)-4 state the following information. phase shift ________ amplitude ________ vertical displacement ______ max y–

Algebra ->  Trigonometry-basics -> SOLUTION: Given the curve y=sin(1/2thetha-90 degrees)-4 state the following information. phase shift ________ amplitude ________ vertical displacement ______ max y–      Log On


   

Question 1091306: Given the curve y=sin(1/2thetha-90 degrees)-4 state the following information.
phase shift ________ amplitude ________ vertical displacement ______
max y–value ________ min y–value ____________ period _________
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
y=sin%281%2F2%28theta%29-90+%29-4+
Use the form+a%2Asin%28bx-c%29%2Bd to find the variables used to find the amplitude, period, phase shift, and vertical shift.
a=1
b=1%2F2
c=90+->pi%2F2+radians
d=-4
the amplitude is a+=1
so, amplitude is:+1

Find the period using the formula 2pi%2Fb=>2pi%2F%281%2F2%29=4pi
period :4+pi
Find the phase shift using the formula c%2Fb
%28pi%2F2%29%2F%281%2F2%29=2pi%2F2=pi->
the phase shift : pi
the vertical shift is d=-4
Vertical Shift: 4 units down
maxy+=+sin%28theta%2F2+-+90%29+-+4+=+-3+ at theta+=+180+%2B+pi+-+4+n+%2Api+ for integer n
miny+=+sin%28theta%2F2+-+90%29+-+4+=+-5 at theta+=+180+-+pi+-+4+n+%2Api for integer n
answer:
phase shift ____pi____ amplitude ___1_____ vertical displacement ___4 units down___
max y–value ___-3+_____ min y–value ____-5________ period ___4+pi______