Arccos Calculator

Need to find an angle from a cosine value? Our Arccos Calculator (cos⁻¹) makes it easy! Just enter a cosine ratio (-1 to 1) and get the angle instantly in degrees or radians. Ideal for students, engineers, and math enthusiasts. Fast, free, and precise

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Results

degrees (deg):
radians (rad):
gradians (gon):
turns (tr):
minutes of arc (arcmin):
seconds of arc (arcsec):
milliradians (mrad):
microradians (μrad):
π radians (× π rad):

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Understanding Arccos Function

Arccos (cos⁻¹) is the inverse of the cosine function. While cosine takes an angle and returns a ratio (adjacent/hypotenuse), arccos takes a ratio (between -1 and 1) and returns the corresponding angle.

Arccos Formula

θ = Resulting angle (in degrees or radians)
Input must be between -1 and 1 (since cosine values can't exceed this range)

How to Find an Angle Using Arccos?

Example
A right triangle has adjacent side = 3 and hypotenuse = 5. Find angle θ.
Identify the Cosine Ratio

Apply Arccos
θ = cos^-1 (0.6)
Calculate (Using Calculator)
In Degrees: = 53.13°
In Radians: = 0.927 rad
Verification:
cos (53.13°) = 0.6

Calculation Example arccosine

Now, here we understand the example of using arccos. To understand this, we have given the image of a right triangle below. In this image, we have given the lengths of two known sides.
The known side lengths are a = 62 and the hypotenuse c = 70. A right triangle is shown at point C.
Now here we are, how can we find angle β at point B using the inverse cosine function? It is simple, here we will use the formula.
We all know the rules of trigonometry here. So we know the rule that, by the definition of the cosine, we know that the cosine of β equals the adjacent side divided by the hypotenuse -
So, cos(β) = a / c = 62 / 70 = 0.885.
Now we will use the inverse function here. Using the inverse function, we will get degrees and radians.
So, β = arccos(0.885) = 27.74° (or 0.4843 in radians).

Common Arccos Values

Frequently Asked Questions (FAQ)

1. Why is the range of input values in the arccos function limited to only -1 to 1?
The angle that is referred to as the cosine of an angle is always between -1 and 1. Hence, for any input of the arccos function to be defined, they have to be within this given range; otherwise, the function is undefined.

2. What is the difference between arccos and cos?
Whereas the cosine label has the property that it accepts an angle and produces a ratio, the arccos label does the converse. It takes a ratio (between -1 and 1) as input and gives the particular angle in return.

3. Is it possible to solve complex numbers with the Arccos Calculator?
Standard Arccos Calculators are typically created for real variables. As for complex numbers, the use of special calculators or certain types of software that correspond to complex arithmetic is necessary.

4. How might students use the arccos function in real-life situations or when undertaking real-life projects?
It finds application in physics for the computation of angles in wave equations, in engineering for the determination of angles in mechanical systems, and in computer graphics for rotation and orientation.

5. Are the online arcs calculated precisely?
This opened up Arccos Calculators that are online to be very accurate; in most cases, the accuracy of the results is indicated in several decimal places. They are beneficial for academic as well as professional applications, mainly because they depend upon algorithms to get exact results.

6. Can the angle results be converted from degrees to radians or from radians to degrees?
Indeed, the majority of Arccos Calculators offer an opportunity to switch between degrees and radians. In this feature, you can have the angle results converted to the required unit without computation.