Example  SEQ.T.3. : Suppose $4* \tan(2x-1) +1 = 9$. Find $x$.
Solution: Since $ A \ne 0$ and $B=2, C=1$, the equation can be solved with $2x-1 =\arctan \frac D A$  where $A=4,B=2,$ and $D=9$. So the key solution is $ x =\frac 12(\arctan( \frac 8{4})+1) =\frac 12( \arctan (2)+1) \approx 1.05$

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The GeoGebra mapping diagram visualizes the steps in the algebra for solving equations of the form  $f(x)=A*trig(Bx-C)+k=D$ with $A,B \ne 0$  and $trig = \sin, \cos$ or $\tan$.

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Comments: You can use the sliders to investigate other examples by $A,B,C$ as well as $k$.
You can move the (red) point labelled D on the right axis of the mapping diagram to change the value of $D$.

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