How do you graph and list the amplitude, period, phase shift for $y = tan (θ - \frac{π}{2}) - 2$ $y=tan(theta-pi/2)-2$ ?

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Answer 1 · 2017-11-19T12:40:44

See below.

Amplitude:

The tangent function has no definable amplitude. This is because:

as $θ \to \frac{π}{2} 8888 tan θ \to \infty$ $theta->pi/2color(white)(8888)tantheta->oo$ which is undefined.

Period:

period of $tan θ = π$ $tantheta=pi$

period of $tan (θ - \frac{π}{2}) - 2 = π$ $tan(theta-pi/2)-2=pi$ ( No change in period )

Phases shift:

Subtracting $\frac{π}{2}$ $pi/2$ from $θ$ $theta$ causes a shift in the positive/right direction by $\frac{π}{2}$ $pi/2$

Plots:

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How do you graph and list the amplitude, period, phase shift for y=tan(theta-pi/2)-2y=tan(θ−π2)−2y=tan(theta-pi/2)-2?