# Evaluate sin(-t)=3/8 , csc(t)

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Take the inverse sine of both sides of the equation to extract from inside the sine.
Evaluate .
Multiply each term in by
Multiply each term in by .
Multiply .
Multiply by .
Multiply by .
Multiply by .
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.
Simplify the expression to find the second solution.
Subtract from .
Multiply each term in by
Multiply each term in by .
Multiply .
Multiply by .
Multiply by .
Multiply by .
The resulting angle of is positive and coterminal with .
Find the period.
The period of the function can be calculated using .
Replace with in the formula for period.
Solve the equation.
The absolute value is the distance between a number and zero. The distance between and is .
Divide by .
Add to every negative angle to get positive angles.
Add to to find the positive angle.
Subtract from .
List the new angles.
The period of the function is so values will repeat every radians in both directions.
, for any integer
Exclude the solutions that do not make true.
, for any integer
Take the base solution.
Replace the variable with in the expression.
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Evaluate sin(-t)=3/8 , csc(t)