Trigonometry Examples

Solve for θ in Degrees 2csc(theta)-3=0
Step 1
Add to both sides of the equation.
Step 2
Divide each term in by and simplify.
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Step 2.1
Divide each term in by .
Step 2.2
Simplify the left side.
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Step 2.2.1
Cancel the common factor of .
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Step 2.2.1.1
Cancel the common factor.
Step 2.2.1.2
Divide by .
Step 3
Take the inverse cosecant of both sides of the equation to extract from inside the cosecant.
Step 4
Simplify the right side.
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Step 4.1
Evaluate .
Step 5
The cosecant 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 6
Subtract from .
Step 7
Find the period of .
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Step 7.1
The period of the function can be calculated using .
Step 7.2
Replace with in the formula for period.
Step 7.3
The absolute value is the distance between a number and zero. The distance between and is .
Step 7.4
Divide by .
Step 8
The period of the function is so values will repeat every degrees in both directions.
, for any integer