Trigonometry Examples

Solve for b 10/(sin(10))=9/(sin(b))
Step 1
Rewrite the equation as .
Step 2
Factor each term.
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Step 2.1
Separate fractions.
Step 2.2
Convert from to .
Step 2.3
Divide by .
Step 2.4
Evaluate .
Step 2.5
Multiply by .
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
The LCM of one and any expression is the expression.
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
Cancel the common factor of .
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Step 4.2.1.1
Cancel the common factor.
Step 4.2.1.2
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 5.2.3
Simplify the right side.
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Step 5.2.3.1
Divide by .
Step 6
Take the inverse sine of both sides of the equation to extract from inside the sine.
Step 7
Simplify the right side.
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Step 7.1
Evaluate .
Step 8
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 9
Subtract from .
Step 10
Find the period of .
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Step 10.1
The period of the function can be calculated using .
Step 10.2
Replace with in the formula for period.
Step 10.3
The absolute value is the distance between a number and zero. The distance between and is .
Step 10.4
Divide by .
Step 11
The period of the function is so values will repeat every degrees in both directions.
, for any integer