Inverse Cos Calculator

Inverse Cosine Formula:

\[ \theta = \arccos\left(\frac{\text{adjacent}}{\text{hypotenuse}}\right) \]

Angle (θ):

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1. What is Inverse Cosine?

The inverse cosine function (arccos) returns the angle whose cosine is a given number. It is the inverse operation of the cosine function and is used to find angles in right triangles when the lengths of the adjacent side and hypotenuse are known.

2. How Does the Calculator Work?

The calculator uses the inverse cosine formula:

\[ \theta = \arccos\left(\frac{\text{adjacent}}{\text{hypotenuse}}\right) \]

Where:

\( \theta \) — The angle in degrees or radians
\( \text{adjacent} \) — Length of the side adjacent to the angle
\( \text{hypotenuse} \) — Length of the hypotenuse
\( \arccos \) — Inverse cosine function

Explanation: The calculator computes the ratio of adjacent to hypotenuse, then applies the inverse cosine function to find the corresponding angle.

3. Importance of Inverse Cosine Calculation

Details: Inverse cosine calculations are essential in trigonometry, geometry, physics, engineering, and computer graphics for determining angles from known side lengths in right triangles.

4. Using the Calculator

Tips: Enter the adjacent side length and hypotenuse length (both must be positive values). The adjacent side must be less than or equal to the hypotenuse. Select whether you want the result in degrees or radians.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of inverse cosine?
A: The inverse cosine function returns values between 0 and π radians (0° to 180°).

Q2: Why must adjacent be ≤ hypotenuse?
A: In a right triangle, the adjacent side cannot be longer than the hypotenuse, so the ratio adjacent/hypotenuse must be between 0 and 1.

Q3: What's the difference between degrees and radians?
A: Degrees and radians are different units for measuring angles. 180° equals π radians. Degrees are more common in everyday use, while radians are preferred in mathematical calculations.

Q4: Can I use this for non-right triangles?
A: No, this calculator is specifically for right triangles. For other triangles, you would need to use the Law of Cosines.

Q5: What if I get an error?
A: Make sure both values are positive numbers and that the adjacent side is not larger than the hypotenuse.