Question

How do you graph $y=3\sin x+1$?

Answer 1

Hint: In these types of questions students must have a clear understanding of the graphs of trigonometric functions. In this first, we draw the graph of sin x. The graph of 3sin x is the graph of sin x with the amplitude increased by a factor of 3. The amplitude of sin x is 1, so the amplitude of 3sin x will be 3.

Complete step by step answer:
In order to solve this question we start by drawing the graph of $y=\sin x$ then we multiply sin x by 3 and add 1 to get the graph of the desired equation which is $y=3\sin x+1$.
First, we start by drawing the graph of the equation $y=\sin x$, we get

Now we multiply sin x by 3, we get the equation $y=3\sin x$.
Now drawing the graph of the equation$y=3\sin x$, we get

Now we add 1 to 3 sin x, we get the equation $y=3\sin x+1$
Now drawing the graph of the equation $y=3\sin x+1$, we get

Hence, it is our required answer.

Note:
 For such a type of question, we should know the graphs of trigonometric functions. We should know the terms like amplitude so that we can easily draw this graph. Trigonometry concepts should be clear to avoid mistakes in such types of questions. In this question we should start by first drawing the graph of the equation $y=\sin x$then we can do the necessary operations to reach the desired equation $y=3\sin x+1$. If we try to draw the graph of the equation $y=3\sin x+1$directly then we can commit errors that will lead to the wrong solution.