Home > Trigonometry > Amplitude, Period and Frequency

How do you find the amplitude, period, and shift for #y= -sin (4/3)x#?

Answer 1

amplitude#=1#
period#=270^@#
phase shift#=#none
vertical shift#=#none

The general equation for a sine graph is:

#y=color(red)asin(color(orange)k(x-color(green)d)+color(blue)c#

where: #color(red)a=|"amplitude"|# #color(orange)k=360^@/("period")# #color(green)d=#phase shift #color(blue)c=#vertical shift

In this case, since the value of #a# is #1#, the amplitude is #1#. It would not be #-1# because the amplitude is always an absolute value, or always positive.

The period is found by substituting the #k# value, #4/3#, into the equation, period#=360^@/k#:

period#=360^@/k# #=360^@/(4/3)# #=360^@-:4/3# #=360^@*3/4# #=color(red)cancelcolor(black)(360^@)^(90^@)*3/color(red)cancelcolor(black)4# #=270^@#

The phase shift is #0# in this case since there is no indication after the #x# variable in the equation.

The vertical shift is #0# in this case since there is no indication at the end of the equation.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.