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Pythagorean Identity 1
sin^2(x)+cos^2(x)=1
Pythagorean Identity 2
tan^2(x)+1=sec^2(x)
Pythagorean Identity 3
1+cot^2(x)=csc^2(x)
Equation
y=Asin(B(x±C))±D
A
Amplitude
B
Frequency
C
Phase shift/vertical shift
D
Midline/horizontal shift
Wavelength/period
The distance it takes to complete one cycle/wave.
Frequency
The number of full periods that fit between 0 and 2π
Asymptote
A line that the function approaches but never reaches. This happens when the function is undefined.
y=sin(x)
Wavy shape, curve passes through at midline at y-axis
y=cos(x)
Wavy shape, curve passes through at maximum at y-axis
y=tan(x)
“Chairs” facing negative numbers, one “chair” passes through midline at y-axis
y=csc(x)
Us and upside down Us, y-axis is asymptote
y=sec(x)
Us and upside down Us, y-axis is NOT asymptote
y=cot(x)
“Chairs” facing positive numbers, no “chair” passes through midline at y-axis
y=sin^-1(x)
Axes switched, single “chair” facing negative numbers, “chair” passes through midline at y-axis
y=cos^-1(x)
Axes switched, single “chair” facing positive numbers, “chair” does NOT passes through midline at y-axis
y=tan^-1(x)
Axes switched, “tipped over chair”, “chair” passes through midline at y-axis
