Trig Graphs Unit 7 Test

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