How to Put Arc in Calculator
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Reviewed by Calculator Editorial Team
Calculating arcs in a calculator involves using inverse trigonometric functions to find angles from known ratios. This guide explains how to properly use arc functions in scientific calculators, including common applications in geometry, physics, and engineering.
What is an Arc in Calculators?
An arc in the context of calculators refers to inverse trigonometric functions. These functions allow you to find angles when you know the ratio of sides in a right triangle. The primary arc functions are:
- arcsin (inverse sine) - Finds the angle when you know the ratio of the opposite side to the hypotenuse
- arccos (inverse cosine) - Finds the angle when you know the ratio of the adjacent side to the hypotenuse
- arctan (inverse tangent) - Finds the angle when you know the ratio of the opposite side to the adjacent side
Arc functions are also known as inverse trigonometric functions. They are essential for solving problems involving angles when you have side length ratios.
How to Use Arc Functions
Step-by-Step Guide
- Enter the known ratio value into your calculator
- Press the appropriate arc function button (2nd function + trig button on most scientific calculators)
- Press the equals (=) button to calculate the angle
- Convert the result to degrees if needed (most calculators default to radians)
Formula: θ = arcsin(opposite/hypotenuse) or θ = arctan(opposite/adjacent)
For example, if you know the opposite side is 3 units and the hypotenuse is 5 units, you would calculate arcsin(3/5) to find the angle.
Arc vs Non-Arc Functions
The main difference between arc and non-arc trigonometric functions is their purpose:
| Function Type | Input | Output | Purpose |
|---|---|---|---|
| Non-Arc (sin, cos, tan) | Angle | Ratio of sides | Find side ratios when angle is known |
| Arc (arcsin, arccos, arctan) | Ratio of sides | Angle | Find angle when side ratios are known |
Non-arc functions are used when you know the angle and need to find side ratios, while arc functions are used when you know side ratios and need to find the angle.
Common Arc Functions
arcsin (inverse sine)
Used when you know the ratio of the opposite side to the hypotenuse. The result is the angle whose sine is equal to the given ratio.
arccos (inverse cosine)
Used when you know the ratio of the adjacent side to the hypotenuse. The result is the angle whose cosine is equal to the given ratio.
arctan (inverse tangent)
Used when you know the ratio of the opposite side to the adjacent side. The result is the angle whose tangent is equal to the given ratio.
Most scientific calculators require you to press the 2nd function button before the trigonometric function button to access arc functions.
Practical Examples
Example 1: Finding an Angle in a Right Triangle
Given a right triangle with opposite side = 4 units and hypotenuse = 5 units, find the angle θ.
- Calculate the ratio: 4/5 = 0.8
- Press 2nd function + sin button (arcsin)
- Enter 0.8 and press equals
- Convert radians to degrees if needed (0.927 radians ≈ 53.13°)
Example 2: Calculating a Roof Angle
If a roof rises 4 feet vertically for every 12 feet horizontally, what is the angle of elevation?
- Calculate the ratio: 4/12 ≈ 0.333
- Press 2nd function + tan button (arctan)
- Enter 0.333 and press equals
- Convert to degrees (0.3218 radians ≈ 18.43°)