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Trigonometry Examples
Step 1
Step 1.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 1.2
Since contains both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part then find LCM for the variable part .
Step 1.3
The LCM is the smallest positive number that all of the numbers divide into evenly.
1. List the prime factors of each number.
2. Multiply each factor the greatest number of times it occurs in either number.
Step 1.4
has factors of and .
Step 1.5
The number is not a prime number because it only has one positive factor, which is itself.
Not prime
Step 1.6
Since has no factors besides and .
is a prime number
Step 1.7
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either number.
Step 1.8
Multiply by .
Step 1.9
The factors for are , which is multiplied by each other times.
occurs times.
Step 1.10
The factor for is itself.
occurs time.
Step 1.11
The factors for are , which is multiplied by each other times.
occurs times.
Step 1.12
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either term.
Step 1.13
Multiply by .
Step 1.14
The LCM for is the numeric part multiplied by the variable part.
Step 2
Step 2.1
Multiply each term in by .
Step 2.2
Simplify the left side.
Step 2.2.1
Rewrite using the commutative property of multiplication.
Step 2.2.2
Cancel the common factor of .
Step 2.2.2.1
Factor out of .
Step 2.2.2.2
Cancel the common factor.
Step 2.2.2.3
Rewrite the expression.
Step 2.2.3
Cancel the common factor of .
Step 2.2.3.1
Cancel the common factor.
Step 2.2.3.2
Rewrite the expression.
Step 2.3
Simplify the right side.
Step 2.3.1
Simplify each term.
Step 2.3.1.1
Rewrite using the commutative property of multiplication.
Step 2.3.1.2
Combine and .
Step 2.3.1.3
Cancel the common factor of .
Step 2.3.1.3.1
Factor out of .
Step 2.3.1.3.2
Cancel the common factor.
Step 2.3.1.3.3
Rewrite the expression.
Step 2.3.1.4
Rewrite using the commutative property of multiplication.
Step 2.3.1.5
Cancel the common factor of .
Step 2.3.1.5.1
Factor out of .
Step 2.3.1.5.2
Factor out of .
Step 2.3.1.5.3
Cancel the common factor.
Step 2.3.1.5.4
Rewrite the expression.
Step 2.3.1.6
Combine and .
Step 2.3.1.7
Cancel the common factor of .
Step 2.3.1.7.1
Cancel the common factor.
Step 2.3.1.7.2
Rewrite the expression.
Step 3
Step 3.1
Rewrite the equation as .
Step 3.2
Move all terms not containing to the right side of the equation.
Step 3.2.1
Subtract from both sides of the equation.
Step 3.2.2
Subtract from .
Step 3.3
Divide each term in by and simplify.
Step 3.3.1
Divide each term in by .
Step 3.3.2
Simplify the left side.
Step 3.3.2.1
Cancel the common factor of .
Step 3.3.2.1.1
Cancel the common factor.
Step 3.3.2.1.2
Divide by .
Step 3.3.3
Simplify the right side.
Step 3.3.3.1
Move the negative in front of the fraction.
Step 4
The result can be shown in multiple forms.
Exact Form:
Decimal Form: