Question

How do you graph $\cos \left( \dfrac{3}{2} \right)x$ ?

Answer 1

Hint: In this question, we have to plot the trigonometric equation of the curve. Therefore, we have to find the slope and intercept of the equation. Thus, we use the slope-intercept form. As we know, the slope is the ratio of the vertical change or horizontal change between any two distinct points on the curve. About intercepts, the x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis. Thus, we compare the general line of the equation and the given equation, to get the value of the slope and intercepts of the equation. After that, draw the graph of the equation using the slope and intercepts, which is our required answer

Complete step by step answer:
In this question, we have to plot the equation $y=\cos \left( \dfrac{3}{2} \right)x$ ----- (1) using slope-intercept form.
As we know, the equation of the line is $y=mx+c$ , where ------- (2)
m is the slope of the equation = $\dfrac{y}{x}=\dfrac{\text{rise}}{\text{run}}$ , means y will go vertically and x will go horizontal
In addition, c is the y-intercept =constant ------------- (1)
As we see the equation (1) has transformed into the general line of equation $y=mx+c$ .
Therefore, on comparing equations (1) and (2), we get that
The slope of the equation $y=\cos \left( \dfrac{3}{2} \right)x$ = $m=0.07073$ , and
The intercept of y-axis $y=\cos \left( \dfrac{3}{2} \right)x$ = $c=0$ .
So, now we will draw a graph using slope $m=0.070703$ and y-intercept $c=0$ or $c=\left( 0,0 \right)$ , that is
First, we plot the y-intercept $c=\left( 0,0 \right)$ of the equation, we get

Now, we plot the slope of the equation $m=0.070703$, which is we raise 0.070703 units from the y-intercept and then run 1 unit, we get

Now, we join points (0,0) and (1,0.070703), to get the required line of equation, that is

Thus, we draw the graph of equation $y=cox\left( \dfrac{3}{2} \right)x$ with slope $m=0.070703$ and y-intercept $c=0$ or $c=\left( 0,0 \right)$.

Note:
Always do proper calculations to get the exact slope and intercept of the equation. Whenever you get fractional intercept, try making them in decimal, it will help you better to draw the graph. You can also find the y-intercept by using the substitution method. Let x=0 in the equation and solve for y, which is the required y-intercept for the answer.