1. What is the Cos A Given Sin A Formula?

The formula \(\cos A = \sqrt{1 - (\sin A)^2}\) is derived from the fundamental Pythagorean identity in trigonometry. It allows calculation of the cosine of an angle when the sine value is known.

2. How Does the Calculator Work?

The calculator uses the trigonometric identity:

Where:

• \(\cos A\) — Cosine of angle A
• \(\sin A\) — Sine of angle A (input value between -1 and 1)
• \(\sqrt{}\) — Square root function

Explanation: This formula is based on the Pythagorean identity \(\sin^2 A + \cos^2 A = 1\), rearranged to solve for cosine.

3. Trigonometric Identity Explanation

Details: The Pythagorean identity states that for any angle A, the square of sine plus the square of cosine equals 1. This relationship forms the basis for calculating one trigonometric function when the other is known.

4. Using the Calculator

Tips: Enter the sine value (between -1 and 1) and click calculate. The calculator will compute the corresponding cosine value using the square root function.

5. Frequently Asked Questions (FAQ)

Q1: Why does the formula use square root?
A: The square root is used because we're solving for cosine from the squared relationship \(\cos^2 A = 1 - \sin^2 A\).

Q2: What are the valid input values?
A: Sine values must be between -1 and 1 inclusive, as these are the possible range of sine function outputs.

Q3: Does this formula work for all angles?
A: Yes, the Pythagorean identity holds true for all real angles, making this formula universally applicable.

Q4: Why might the result be positive or negative?
A: The calculator returns the principal (positive) square root. In practice, the sign of cosine depends on the quadrant of the angle.

Q5: What functions are used in this calculation?
A: This formula uses the square root function (sqrt) and operates on two variables: Cos A and Sin A.