# Find the Exact Value sec(arcsin(minus one divide two))

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 .

One raised to any power equals one.

Apply the power rule for exponent distribution.

Apply the product rule to .

Use the product rule for .

First, multiply by by adding the exponents.

Move .

Multiply by .

Raise to the power of .

Use the power rule to Add exponents.

Add and .

Raise to the power of .

One to any power is one.

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 .

Add.

Multiply by .

Add numerators over the common denominator.

Clarify the numerator.

First, multiply by .

Subtract from .

Should be rewritten as .

Clarify the denominator.

Rewrite as .

Withdraw terms from under the radical, assuming positive real numbers.

Multiply the numerator by the denominator's reciprocal.

Multiply by .

Multiply by .

Multiply and .

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Rewrite as .

Rewrite as .

Use the power rule when multiplying the exponents, .

Combine and .

The common factor should be canceled of .

Cancel the common factor.

First, divide by .

Solve the exponent.

The result can be displayed in a variety of ways.

Exact Form:

Decimal Form:

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