Calculator Inputs
Plotly Graph
The graph shows the principal arc cosine curve across the selected input range.
Example Data Table
These sample values show the principal inverse cosine output in both radians and degrees.
| Input x | arccos(x) in Radians | arccos(x) in Degrees |
|---|---|---|
| -1 | 3.141593 | 180° |
| -0.5 | 2.094395 | 120° |
| 0 | 1.570796 | 90° |
| 0.5 | 1.047198 | 60° |
| 1 | 0 | 0° |
Formula Used
Arc cosine returns the principal angle whose cosine equals the input value. For an input x, the calculator evaluates the inverse trigonometric relation below.
Primary formula: θ = arccos(x)
Check formula: cos(θ) = x
Degree conversion: Degrees = Radians × 180 / π
Domain: -1 ≤ x ≤ 1 | Principal range: 0 ≤ θ ≤ π
Because arc cosine is the inverse of cosine on its principal interval, the output angle always stays within that fixed range. The graph therefore decreases from π to 0 radians as x moves from -1 to 1.
How to Use This Calculator
- Enter an input value between -1 and 1.
- Select whether you want the main answer shown in degrees or radians.
- Choose the number of decimal places for display.
- Optionally add batch values to compute several arc cosine results together.
- Set the plot start, plot end, and sample count.
- Click Calculate Arc Cosine to show the result above the form.
- Review the table, graph, and cosine verification value.
- Use the CSV or PDF buttons to export your calculated dataset.
FAQs
1. What does arc cosine calculate?
It finds the principal angle whose cosine equals the given input. For example, arccos(0.5) returns 60° or 1.047198 radians.
2. Why must the input stay between -1 and 1?
Cosine values for real angles always lie from -1 to 1. Inputs outside that interval do not produce real arc cosine outputs.
3. What range does the result use?
The principal arc cosine result is always between 0 and π radians. In degrees, that means every answer stays between 0° and 180°.
4. Can I get both radians and degrees?
Yes. The summary highlights your selected unit, while the result table still shows both radians and degrees for easier comparison.
5. What is the cosine check used for?
It verifies the answer by applying cosine to the computed angle. A matching value confirms that the inverse calculation is behaving correctly.
6. Why does the graph slope downward?
On the principal interval, arc cosine decreases as x increases. Inputs near -1 produce large angles, while inputs near 1 produce small angles.
7. What is the batch input section for?
It lets you calculate several arc cosine values at once. This is useful for tables, assignments, engineering checks, or exporting grouped results.
8. Do exports include my current results?
Yes. After a successful calculation, the CSV and PDF buttons export the current result table so you can save or share it easily.