Finite Math Examples

Find the Roots (Zeros) y=4cos(3x+pi/2)
Step 1
Set equal to .
Step 2
Solve for .
Tap for more steps...
Step 2.1
Divide each term in by and simplify.
Tap for more steps...
Step 2.1.1
Divide each term in by .
Step 2.1.2
Simplify the left side.
Tap for more steps...
Step 2.1.2.1
Cancel the common factor of .
Tap for more steps...
Step 2.1.2.1.1
Cancel the common factor.
Step 2.1.2.1.2
Divide by .
Step 2.1.3
Simplify the right side.
Tap for more steps...
Step 2.1.3.1
Divide by .
Step 2.2
Take the inverse cosine of both sides of the equation to extract from inside the cosine.
Step 2.3
Simplify the right side.
Tap for more steps...
Step 2.3.1
The exact value of is .
Step 2.4
Move all terms not containing to the right side of the equation.
Tap for more steps...
Step 2.4.1
Subtract from both sides of the equation.
Step 2.4.2
Combine the numerators over the common denominator.
Step 2.4.3
Subtract from .
Step 2.4.4
Divide by .
Step 2.5
Divide each term in by and simplify.
Tap for more steps...
Step 2.5.1
Divide each term in by .
Step 2.5.2
Simplify the left side.
Tap for more steps...
Step 2.5.2.1
Cancel the common factor of .
Tap for more steps...
Step 2.5.2.1.1
Cancel the common factor.
Step 2.5.2.1.2
Divide by .
Step 2.5.3
Simplify the right side.
Tap for more steps...
Step 2.5.3.1
Divide by .
Step 2.6
The cosine function is positive in the first and fourth quadrants. To find the second solution, subtract the reference angle from to find the solution in the fourth quadrant.
Step 2.7
Solve for .
Tap for more steps...
Step 2.7.1
Simplify .
Tap for more steps...
Step 2.7.1.1
To write as a fraction with a common denominator, multiply by .
Step 2.7.1.2
Combine fractions.
Tap for more steps...
Step 2.7.1.2.1
Combine and .
Step 2.7.1.2.2
Combine the numerators over the common denominator.
Step 2.7.1.3
Simplify the numerator.
Tap for more steps...
Step 2.7.1.3.1
Multiply by .
Step 2.7.1.3.2
Subtract from .
Step 2.7.2
Move all terms not containing to the right side of the equation.
Tap for more steps...
Step 2.7.2.1
Subtract from both sides of the equation.
Step 2.7.2.2
Combine the numerators over the common denominator.
Step 2.7.2.3
Subtract from .
Step 2.7.2.4
Cancel the common factor of .
Tap for more steps...
Step 2.7.2.4.1
Cancel the common factor.
Step 2.7.2.4.2
Divide by .
Step 2.7.3
Divide each term in by and simplify.
Tap for more steps...
Step 2.7.3.1
Divide each term in by .
Step 2.7.3.2
Simplify the left side.
Tap for more steps...
Step 2.7.3.2.1
Cancel the common factor of .
Tap for more steps...
Step 2.7.3.2.1.1
Cancel the common factor.
Step 2.7.3.2.1.2
Divide by .
Step 2.8
Find the period of .
Tap for more steps...
Step 2.8.1
The period of the function can be calculated using .
Step 2.8.2
Replace with in the formula for period.
Step 2.8.3
The absolute value is the distance between a number and zero. The distance between and is .
Step 2.9
The period of the function is so values will repeat every radians in both directions.
, for any integer
Step 2.10
Consolidate the answers.
, for any integer
, for any integer
Step 3