Find the Exact Value cot(arcsin(3/5))

Find the Exact Value cot(arcsin(3/5))
Draw a triangle in the plane with vertices , , and the origin. Then is the angle between the positive x-axis and the ray beginning at the origin and passing through . Therefore, is .
Multiply the numerator by the reciprocal of the denominator.
One to any power is one.
Apply the product rule to .
Raise to the power of .
Raise to the power of .
Write as a fraction with a common denominator.
Combine the numerators over the common denominator.
Subtract from .
Rewrite as .
Simplify the numerator.
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Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Simplify the denominator.
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Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Simplify terms.
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Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Combine and .
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Mixed Number Form:
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