SOLUTION: What is the graph of one cycle of a sine curve with the given characteristics? Using the form y=a sin b theta, that is an equation for the sine curve? Amplitude = 4, period 1/4 pi

Algebra ->  Trigonometry-basics -> SOLUTION: What is the graph of one cycle of a sine curve with the given characteristics? Using the form y=a sin b theta, that is an equation for the sine curve? Amplitude = 4, period 1/4 pi      Log On


   

Question 969921: What is the graph of one cycle of a sine curve with the given characteristics? Using the form y=a sin b theta, that is an equation for the sine curve?
Amplitude = 4, period 1/4 pi, and a < 0
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
The amplitude is the absolute value of a: that is abs%28a%29, and it is given that a+%3C+0; so, if your amplitude is 4, but a is less than zero, we have to use -4 for a.
a=-4
If our period is usually 2pi, and in this case it is %281%2F4%29pi=pi%2F4, everything has to go 8 times as fast, so b=+8.
That will give us a function:
y=-4%2Asin%28+8%2A+theta%29

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C-4%2Asin%28+8%2A+x%29%29+