Trigonometry Examples

Solve for t sin(-t)=3/4
Step 1
Take the inverse sine of both sides of the equation to extract from inside the sine.
Step 2
Simplify the right side.
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Step 2.1
Evaluate .
Step 3
Divide each term in by and simplify.
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Step 3.1
Divide each term in by .
Step 3.2
Simplify the left side.
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Step 3.2.1
Dividing two negative values results in a positive value.
Step 3.2.2
Divide by .
Step 3.3
Simplify the right side.
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Step 3.3.1
Divide by .
Step 4
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 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
Dividing two negative values results in a positive value.
Step 5.2.2
Divide by .
Step 5.3
Simplify the right side.
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Step 5.3.1
Combine the numerators over the common denominator.
Step 5.3.2
Simplify the expression.
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Step 5.3.2.1
Subtract from .
Step 5.3.2.2
Divide by .
Step 6
Find the period of .
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Step 6.1
The period of the function can be calculated using .
Step 6.2
Replace with in the formula for period.
Step 6.3
The absolute value is the distance between a number and zero. The distance between and is .
Step 6.4
Divide by .
Step 7
Add to every negative angle to get positive angles.
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Step 7.1
Add to to find the positive angle.
Step 7.2
Subtract from .
Step 7.3
Add to to find the positive angle.
Step 7.4
Subtract from .
Step 7.5
List the new angles.
Step 8
The period of the function is so values will repeat every radians in both directions.
, for any integer