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Arccos Function:
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The arccos function, denoted as cos⁻¹(x) or arccos(x), is the inverse of the cosine function. It returns the angle whose cosine is the given number x. The result is typically expressed in radians or degrees, with the principal value ranging from 0 to π radians (0° to 180°).
The calculator uses the arccos function:
Where:
Explanation: The calculator takes a cosine value between -1 and 1 and returns the corresponding angle in degrees, using the mathematical inverse cosine function.
Details: The arccos function is widely used in trigonometry, geometry, physics, engineering, and computer graphics. It helps determine angles when the cosine value is known, which is essential in solving triangles, analyzing waveforms, and calculating rotations.
Tips: Enter a value between -1 and 1 in the input field. The calculator will return the corresponding angle in degrees. Ensure the input is within the valid range to get accurate results.
Q1: What is the range of valid inputs for arccos?
A: The input x must be between -1 and 1, inclusive. Values outside this range are mathematically undefined for the arccos function.
Q2: In what units is the result returned?
A: The calculator returns the angle in degrees. If you need radians, you can convert using the formula: radians = degrees × π/180.
Q3: What is the principal value range of arccos?
A: The principal value of arccos ranges from 0° to 180° (0 to π radians). This means the result will always be in this range.
Q4: Can arccos be used for complex numbers?
A: This calculator handles only real numbers. For complex numbers, specialized mathematical software or libraries are required.
Q5: How is arccos related to other inverse trigonometric functions?
A: Arccos is one of the main inverse trigonometric functions, along with arcsin and arctan. They are all related through various trigonometric identities and can often be used interchangeably with appropriate adjustments.