# How do you find the amplitude, period, vertical and phase shift and graph y=2/5tan(6theta+135)-4?

Oct 31, 2016

$y$ / $f \left(x\right) = A f \left(B x - C\right) + D$ where,
$f$: trig functions (sin,cos,etc)
$A$: amplitude is A
$B$: period is (2π)/|B|
$C$: phase shift is C/B
$D$: vertical shift is D
*x is interchangible with θ
See: http://www.purplemath.com/modules/grphtrig.htm

#### Explanation:

$y$ / $f \left(x\right) = A f \left(B x - C\right) + D$
So, in $y = \frac{2}{5} \tan \left(6 \theta + 135\right) - 4$, we have
Amplitude = $\frac{2}{5}$
Period=$\frac{2 \pi}{|} 6 | = \frac{\pi}{3}$
Phase Shift = $- \frac{135}{6} = - \frac{45}{2}$
Vertical Shift = -4