Finite Math Examples

Find the x and y Intercepts (sin(x))/x
Step 1
Write as an equation.
Step 2
Find the x-intercepts.
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Step 2.1
To find the x-intercept(s), substitute in for and solve for .
Step 2.2
Solve the equation.
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Step 2.2.1
Set the numerator equal to zero.
Step 2.2.2
Solve the equation for .
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Step 2.2.2.1
Take the inverse sine of both sides of the equation to extract from inside the sine.
Step 2.2.2.2
Simplify the right side.
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Step 2.2.2.2.1
The exact value of is .
Step 2.2.2.3
The sine function is positive in the first and second quadrants. To find the second solution, subtract the reference angle from to find the solution in the second quadrant.
Step 2.2.2.4
Subtract from .
Step 2.2.2.5
Find the period of .
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Step 2.2.2.5.1
The period of the function can be calculated using .
Step 2.2.2.5.2
Replace with in the formula for period.
Step 2.2.2.5.3
The absolute value is the distance between a number and zero. The distance between and is .
Step 2.2.2.5.4
Divide by .
Step 2.2.2.6
The period of the function is so values will repeat every radians in both directions.
, for any integer
, for any integer
Step 2.2.3
Consolidate the answers.
, for any integer
, for any integer
Step 2.3
x-intercept(s) in point form.
x-intercept(s): , for any integer
x-intercept(s): , for any integer
Step 3
Find the y-intercepts.
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Step 3.1
To find the y-intercept(s), substitute in for and solve for .
Step 3.2
The equation has an undefined fraction.
Undefined
Step 3.3
To find the y-intercept(s), substitute in for and solve for .
y-intercept(s):
y-intercept(s):
Step 4
List the intersections.
x-intercept(s): , for any integer
y-intercept(s):
Step 5