How do I find the equation of a cosine function with a maximum of 3, a minimum of -3, and a period of 4?
+118690 How do I find the equation of a cosine function with a maximum of 3, a minimum of -3, and a period of 4?
lets see
y=3cos b(x+c)
c can be any constant becasue you have not mentioned phase shift.
where period = 2pi/b
\(\frac{2\pi}{b}=4\\ \frac{\pi}{b}=2\\ b=\frac{\pi}{2}\)
so it is
\(y=3cos[\frac{\pi }{2}(x+c)]\)
check (here is your graph )
+118690 This is what you must remember.
\(y=a*cos[b(x+c)]+d\\~\\ \text{a is the amplitude}\\ \text{d is the vertical shift}\\ \text{c is the horizontal, or phase, shift}\\ \text{and last but not least, the period is}\frac{2\pi}{b}\\ \text{The angle is in radians}\\ \)
If you remember that then these questions become almost trivia.
Sine functions work the same way.
