# Find the Exact Value tan(arcsin(-4/5))

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.
Simplify the denominator.
One to any power is one.
Use the power rule to distribute the exponent.
Apply the product rule to .
Apply the product rule to .
Multiply by by adding the exponents.
Move .
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Raise to the power of .
Raise to the power of .
Raise to the power of .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Subtract from .
Rewrite as .
Simplify the numerator.
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Simplify the denominator.
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Multiply the numerator by the reciprocal of the denominator.
Multiply by .
Cancel the common factor of .
Move the leading negative in into the numerator.
Cancel the common factor.
Rewrite the expression.
Combine and .
Move the negative in front of the fraction.
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Mixed Number Form:
Find the Exact Value tan(arcsin(-4/5))