Question

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

Answer 1

`y` / `f(x)=Af(Bx-C)+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(x)=Af(Bx-C)+D`
So, in `y=2/5tan(6theta+135)-4`, we have
Amplitude = `2/5`
Period=`(2pi)/|6| = pi/3`
Phase Shift = `-135/6 =-45/2`
Vertical Shift = -4