I need to draw a correct sketch of trigonometric graphs like $$y=2\sin \left(3x+\frac{\pi}{4}\right)-1$$
I usually transform this into $$Y=\sin X$$ , where $$Y=\frac{y+1}{2}$$ and $$X=3x+\frac{\pi}{4}$$
And draw the graph $Y$ vs $X$.
Is there another method which will help me to draw the graph in one step ?
Best Answer
When someone gives me this type of function to draw, I think like this:
First, I draw $\sin(x)$ between $0$ and $2\pi$:
Then I draw $\sin(3x)$:
Then I draw $\sin\left(3x+\dfrac{\pi}{4}\right)$, which means I have to move $\sin(3x)$ to the left. How much? $\pi/12$ radians:
I draw $2\sin\left( 3x+\dfrac{\pi}{4} \right)$:
The last step is to draw $2\sin\left( 3x+\dfrac{\pi}{4} \right) -1$, which means the figure will go down:
If you want to draw trigonometric functions in one step, you could learn these steps, next you could go through each step mentally, and after that you draw the last step in paper.