Trigonometric Graphs Flashcards: Sin, Cos, Tan

Question 1

What is the basic graph of $y=\sin x$ (key features)?

Accepted Answer

A smooth wave through $(0,0)$ with amplitude $1$ and period $2\pi$; max at $(\frac{\pi}{2},1)$ and min at $(\frac{3\pi}{2},-1)$.

Question 2

State the general transformed sine/cosine form with phase shift and vertical shift.

Accepted Answer

$$y=A\sin(B(x-C))+D\quad	ext{or}\quad y=A\cos(B(x-C))+D$$ $C$ is the phase shift (right if $C>0$), and $D$ is the vertical shift (midline $y=D$).

Question 3

State the period and asymptotes for $y=	an(B(x-C))+D$.

Accepted Answer

$$	ext{Period} = \frac{\pi}{|B|}$$ Vertical asymptotes when $B(x-C)=\frac{\pi}{2}+k\pi$, i.e. $$x=C+\frac{\frac{\pi}{2}+k\pi}{B}$$ Midline is $y=D$.

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