Question

How do you graph $y = - \sin x$?

Answer 1

Here, we are required to explain how the graph of $y = - \sin x$ is drawn. Thus, we will state the process of plotting the graph of the given function. Then, we will observe the difference in the graphs of positive and negative $\sin x$. This will help us to find how the required graph of $y = - \sin x$ is drawn. Hence, this will be our required answer.

Complete step by step solution:
We know that the graph of $y = \sin x$ is like a wave starting from the origin or in other words, which cuts the $x$ axis at point $\left( {0,0} \right)$ due to the fact that $\sin 0^\circ = 0$, hence, at 0, the value of sine is 0. Also, the value of sine lies from $- 1$ to 1. Thus, this wave which is showing the sine function oscillates from $- 1$ to 1 and it repeats its value after every $180^\circ$ or $2\pi$ units.
The domain of the sine function is all real numbers but the range is $\left[ { - 1,1} \right]$
Now, when we graph $y = - \sin x$ then, the graph is reflected across the $x$ axis. Else, everything remains the same. And since the graph is reflected across the $x$ axis, therefore, the values of $x$ coordinates remain the same but in front of the $y$ coordinates, we have to add a negative sign.

Therefore, the graph $y = - \sin x$ is the same as the graph of $y = \sin x$ just it is reflected across the $x$ axis or in other words it is an image of the graph of $\sin x$.

Note:
In this question, we have used trigonometry. Trigonometry is a branch of mathematics that helps us to study the relationship between the sides and the angles of a triangle. In practical life, trigonometry is used by cartographers (to make maps). It is also used by the aviation and naval industries. In fact, trigonometry is even used by Astronomers to find the distance between two stars. Hence, it has an important role to play in everyday life. The three most common trigonometric functions are the tangent function, the sine, and the cosine function. In simple terms, they are written as ‘sin’, ‘cos’, and ‘tan’. Hence, trigonometry is not just a chapter to study, in fact, it is being used in everyday life.