Trigonometry Examples

Solve for x 670/4020=201/16-67/(32(670/4020))+67/(13sin(x))
Step 1
Rewrite the equation as .
Step 2
Move all terms not containing to the right side of the equation.
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Step 2.1
Subtract from both sides of the equation.
Step 2.2
Add to both sides of the equation.
Step 2.3
Simplify each term.
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Step 2.3.1
Cancel the common factor of and .
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Step 2.3.1.1
Factor out of .
Step 2.3.1.2
Cancel the common factors.
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Step 2.3.1.2.1
Factor out of .
Step 2.3.1.2.2
Cancel the common factor.
Step 2.3.1.2.3
Rewrite the expression.
Step 2.3.2
Cancel the common factor of and .
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Step 2.3.2.1
Factor out of .
Step 2.3.2.2
Cancel the common factors.
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Step 2.3.2.2.1
Factor out of .
Step 2.3.2.2.2
Cancel the common factor.
Step 2.3.2.2.3
Rewrite the expression.
Step 2.3.3
Combine and .
Step 2.3.4
Cancel the common factor of and .
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Step 2.3.4.1
Factor out of .
Step 2.3.4.2
Cancel the common factors.
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Step 2.3.4.2.1
Factor out of .
Step 2.3.4.2.2
Cancel the common factor.
Step 2.3.4.2.3
Rewrite the expression.
Step 2.3.5
Multiply the numerator by the reciprocal of the denominator.
Step 2.3.6
Multiply .
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Step 2.3.6.1
Combine and .
Step 2.3.6.2
Multiply by .
Step 2.4
Combine the numerators over the common denominator.
Step 2.5
Add and .
Step 2.6
Divide by .
Step 2.7
Add and .
Step 3
Find the LCD of the terms in the equation.
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Step 3.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 3.2
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 3.3
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 3.4
Since has no factors besides and .
is a prime number
Step 3.5
has factors of and .
Step 3.6
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either number.
Step 3.7
Multiply .
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Step 3.7.1
Multiply by .
Step 3.7.2
Multiply by .
Step 3.8
The factor for is itself.
occurs time.
Step 3.9
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either term.
Step 3.10
The LCM for is the numeric part multiplied by the variable part.
Step 4
Multiply each term in by to eliminate the fractions.
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Step 4.1
Multiply each term in by .
Step 4.2
Simplify the left side.
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Step 4.2.1
Rewrite using the commutative property of multiplication.
Step 4.2.2
Cancel the common factor of .
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Step 4.2.2.1
Factor out of .
Step 4.2.2.2
Factor out of .
Step 4.2.2.3
Cancel the common factor.
Step 4.2.2.4
Rewrite the expression.
Step 4.2.3
Combine and .
Step 4.2.4
Multiply by .
Step 4.2.5
Cancel the common factor of .
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Step 4.2.5.1
Cancel the common factor.
Step 4.2.5.2
Rewrite the expression.
Step 4.3
Simplify the right side.
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Step 4.3.1
Cancel the common factor of .
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Step 4.3.1.1
Factor out of .
Step 4.3.1.2
Cancel the common factor.
Step 4.3.1.3
Rewrite the expression.
Step 5
Solve the equation.
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Step 5.1
Rewrite the equation as .
Step 5.2
Divide each term in by and simplify.
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Step 5.2.1
Divide each term in by .
Step 5.2.2
Simplify the left side.
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Step 5.2.2.1
Cancel the common factor of .
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Step 5.2.2.1.1
Cancel the common factor.
Step 5.2.2.1.2
Divide by .
Step 6
The range of sine is . Since does not fall in this range, there is no solution.
No solution