How do you find the important points to graph $y = 3 tan (4 x - \frac{π}{3})$ $y=3 tan (4x-pi/3)$ ?

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Answer 1 · 2018-07-11T03:41:51

See explanation and graphs.

The period of $tan (k x + c) = \frac{π}{k}$ $tan ( k x + c ) = pi/k$ .

So, the period of $y = \frac{π}{4} = 0.7854$ $y = pi/4 = 0.7854$ , nearly, and $\frac{π}{3} = 1.0472$ $pi/3 = 1.0472$ ,

nearly..

As $4 x - pi/3 to ( 2 k + 1 )pi/2, y to +- oo, k = 0, +-1, +-2, +-3, ...$ .

Upon setting $k = - 1 and 0$ , one period about origin is

$x in ( - pi/24, 5pi/24 ) = ( - 0.1309, 0.6545 )$ , nearly.

Direct graph for 10 periods, $x in ( 0, 7.854 0 3.927)$

(Slide the graph ( $larr$ ) to see further periods)
graph{y - 3 tan ( 4 x - 1.0472 ) = 0[ 0 7.854 0 3.927] ]}

The inverse is $x = 1/4(arctan( y/3 ) +pi/3 )$

One-period graph using the inverse:
graph{x - 1/4(arctan( y/3 ) + 1.0472) = 0}

How do you find the important points to graph y=3 tan (4x-pi/3)y=3tan(4x−π3)y=3 tan (4x-pi/3)?