Trigonometry Examples

Solve for x 1/32*((100)^2sin(2x))=300
Step 1
Multiply both sides of the equation by .
Step 2
Simplify both sides of the equation.
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Step 2.1
Simplify the left side.
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Step 2.1.1
Simplify .
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Step 2.1.1.1
Combine and .
Step 2.1.1.2
Raise to the power of .
Step 2.1.1.3
Cancel the common factor of and .
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Step 2.1.1.3.1
Factor out of .
Step 2.1.1.3.2
Cancel the common factors.
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Step 2.1.1.3.2.1
Factor out of .
Step 2.1.1.3.2.2
Cancel the common factor.
Step 2.1.1.3.2.3
Rewrite the expression.
Step 2.1.1.4
Multiply the numerator by the reciprocal of the denominator.
Step 2.1.1.5
Simplify the expression.
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Step 2.1.1.5.1
Multiply by .
Step 2.1.1.5.2
Raise to the power of .
Step 2.1.1.6
Cancel the common factor of .
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Step 2.1.1.6.1
Factor out of .
Step 2.1.1.6.2
Cancel the common factor.
Step 2.1.1.6.3
Rewrite the expression.
Step 2.1.1.7
Combine and .
Step 2.1.1.8
Combine and .
Step 2.1.1.9
Combine and .
Step 2.1.1.10
Multiply by .
Step 2.1.1.11
Cancel the common factor of .
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Step 2.1.1.11.1
Cancel the common factor.
Step 2.1.1.11.2
Divide by .
Step 2.2
Simplify the right side.
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Step 2.2.1
Simplify .
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Step 2.2.1.1
Combine and .
Step 2.2.1.2
Raise to the power of .
Step 2.2.1.3
Cancel the common factor of and .
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Step 2.2.1.3.1
Factor out of .
Step 2.2.1.3.2
Cancel the common factors.
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Step 2.2.1.3.2.1
Factor out of .
Step 2.2.1.3.2.2
Cancel the common factor.
Step 2.2.1.3.2.3
Rewrite the expression.
Step 2.2.1.4
Multiply the numerator by the reciprocal of the denominator.
Step 2.2.1.5
Multiply by .
Step 2.2.1.6
Cancel the common factor of .
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Step 2.2.1.6.1
Factor out of .
Step 2.2.1.6.2
Factor out of .
Step 2.2.1.6.3
Cancel the common factor.
Step 2.2.1.6.4
Rewrite the expression.
Step 2.2.1.7
Combine and .
Step 2.2.1.8
Multiply by .
Step 3
Take the inverse sine of both sides of the equation to extract from inside the sine.
Step 4
Simplify the right side.
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Step 4.1
Evaluate .
Step 5
Divide each term in by and simplify.
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Step 5.1
Divide each term in by .
Step 5.2
Simplify the left side.
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Step 5.2.1
Cancel the common factor of .
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Step 5.2.1.1
Cancel the common factor.
Step 5.2.1.2
Divide by .
Step 5.3
Simplify the right side.
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Step 5.3.1
Divide by .
Step 6
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 7
Solve for .
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Step 7.1
Subtract from .
Step 7.2
Divide each term in by and simplify.
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Step 7.2.1
Divide each term in by .
Step 7.2.2
Simplify the left side.
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Step 7.2.2.1
Cancel the common factor of .
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Step 7.2.2.1.1
Cancel the common factor.
Step 7.2.2.1.2
Divide by .
Step 7.2.3
Simplify the right side.
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Step 7.2.3.1
Divide by .
Step 8
Find the period of .
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Step 8.1
The period of the function can be calculated using .
Step 8.2
Replace with in the formula for period.
Step 8.3
The absolute value is the distance between a number and zero. The distance between and is .
Step 8.4
Cancel the common factor of .
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Step 8.4.1
Cancel the common factor.
Step 8.4.2
Divide by .
Step 9
The period of the function is so values will repeat every radians in both directions.
, for any integer