Find the x and y Intercepts f(x)=sin(x)

Problem

ƒ(x)=sin(x)

Solution

1. Find the y-intercept by evaluating the function at x=0

y=sin(0)

y=0

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

(0,0)

3. Find the x-intercepts by setting the function equal to zero and solving for x

sin(x)=0

4. Apply the general solution for the sine function, noting that sine is zero at all integer multiples of π

x=n*π

where *n* is any integer *(n∈ℤ)

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

(n*π,0)

Final Answer

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

Want more problems? Check here!