Question

What is the y-intercept of the graph of y=cosx?

Answer 1

We need to find the y-intercept of the graph y=cosx. The y- intercept is the point where the graph of the function crosses the y-axis. The value of the y-intercept is found by simply substituting $x=0$ in the equation $y=\cos x$.

Complete step by step answer:
We are given a function $y=\cos x$ and are asked to find the value of the y-intercept of the function. We will be solving the given question by substituting $x=0$ in the equation $y=\cos x$
The cartesian coordinates plane consists of two-axis perpendicular to each other.
The horizontal axis is referred to as the x-axis and the vertical axis is referred to as the y-axis.
The origin is the intersection of the x-axis and y-axis.
The coordinates of the cartesian plane are usually represented as $\left( x,y \right)$
The first number x denotes the distance of the point along the x-axis
The second number y denotes the distance of the point along the y-axis.
The y-intercept is the point where the graph of the function crosses the y-axis. The point lies on the y-axis.
Hence, the coordinates of the y-intercept are given by $\left( x,y \right)$ where the value of $x=0$
According to our question,
We need to find the value of the y-intercept of the graph
$\Rightarrow y=\cos x$
The y-intercept of the above graph can be found by substituting the value of x as zero.
Substituting $x=0$ in the above equation, we get,
$\Rightarrow y=\cos \left( 0 \right)$
From trigonometry, we know that $\cos \left( 0 \right)=1$
Substituting the same, we get,
$\Rightarrow y=1$
$\therefore$ The y-intercept of the graph y=cosx is 1.

Note: The value of the y-intercept of the graph can be found out by plotting a graph of the function $y=\cos x$
The graph of the function is represented as follows,

From the above graph, the graph of the function crosses the y-axis at the point $A\left( 0,1 \right)$
Hence, the value of the y-intercept of the graph is equal to one.