Find the x and y Intercepts y=cos(x)

Problem

y=cos(x)

Solution

1. Find the y-intercept by setting x=0 in the equation.

cos(0)=1

y=1

2. Identify the y-intercept coordinate as the point where the graph crosses the vertical axis.

(0,1)

3. Find the x-intercepts by setting y=0 and solving for x

cos(x)=0

4. Solve the trigonometric equation for x by identifying the values where the cosine function equals zero.

x=π/2+n*π

where *n* is any integer.

5. Identify the x-intercept coordinates as the set of points where the graph crosses the horizontal axis.

(π/2+n*π,0)

Final Answer

y-intercept: *(0,1), x-intercepts: *(π/2+n*π,0)* for *n∈ℤ

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