Arcsin 14/20
2026-02-21 20:31 Diff
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Last updated on December 11, 2025

Arcsin 14/20 equals approximately 0.7227 radians. It is the inverse of the sine function, giving the angle whose sine value is 14/20 (or 0.7), which can be seen from the unit circle at point (cos x, sin x).

What is Arcsin 14/20?

Arcsin 14/20 represents the angle whose sine value equals 14/20 or 0.7.

Since sine and arcsin are inverse functions defined as arcsin: [-1, 1] → [-π/2, π/2] and sin: [-90°, 90°] → [-1, 1], this means that if sin x = y, then x = arcsin(y).

From the trigonometry table, we know that arcsin 0.7 is approximately 0.7227 radians or 41.81°.

Therefore, by the definition of the sine inverse, the value of arcsin 14/20 is approximately 0.7227 radians or 41.81°.

Arcsin 14/20 in Degrees

The arcsin function is defined as arcsin: [-1, 1] → [-90°, 90°], which means its domain is [-1, 1] and its range is [-90°, 90°]; since the sine function is periodic, sin θ = 0.7 for several angles, but only one angle lies within the principal interval [-90°, 90°].

Therefore, arcsin(14 ÷ 20) = 41.81°(approx)

Arcsin 14/20 in Radians

As we know, the principal branch of arcsin is defined as arcsin: [-1, 1] to [-π/2, π/2], where [-π/2, π/2] represents the range of the sine inverse function.

Therefore, using a trigonometry table, we can write arcsin(14 ÷ 20) = θ, such that sin θ = 0.7

Hence, θ ≈ 0.7227 radians. Thus, the value of arcsin 14/20 is approximately 0.7227 radians.

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Tips and Tricks for Arcsin 14/20

The concept of arcsin 14/20 can be tricky to understand at first.

Here are a few tips and tricks to help learn and remember it.

Arcsin returns the angle whose sine equals the given value.

The sine equals 0.7 at the point (√(1 − 0.7²), 0.7) within the range [ -90° to 90°] (or -π/2 to π/2).

Since sin 41.81° = 0.7(approx), arcsin(14 ÷ 20) = 41.81°(approx) (or 0.7227 radians), and practicing conversions between radians and degrees helps remember it.

Common Mistakes and How to Avoid Them on Arcsin 14/20

At times, even basic ideas like arcsin 14/20 can cause confusion.

Here’s a list of mistakes students might make while finding arcsin 14/20, along with ways to avoid them.

Problem 1

Find arcsin 14/20.

Okay, lets begin

Approximately 41.81° or 0.7227 radians.

Explanation

Arcsin 14/20 is the angle whose sine is 0.7, which can be found using a calculator to give approximately 41.81° or 0.7227 radians within the range (-90° to 90°) to (-π/2 to π/2).

Well explained 👍

Problem 2

If \(\sin \theta = 0.7\), find \(\theta\) using arcsin.

Okay, lets begin

Approximately 41.81° or 0.7227 radians.

Explanation

By definition, θ = arcsin 0.7.

The arcsin function has a principal range of (-π/2 to π/2) or (-90° to 90°), and since sin θ = 0.7 at θ = 41.81°(approx.) or 0.7227 radians; this value lies within the range.

Well explained 👍

Problem 3

Express arcsin 14/20 in radians.

Okay, lets begin

Approximately 0.7227 radians.

Explanation

Arcsin 14/20 gives the angle whose sine is 0.7.

From a calculator or sine table, sin 0.7227 = 0.7(approx.), so arcsin(14 ÷ 20) = 0.7227 radians (approx.)

Well explained 👍

Problem 4

Express arcsin 14/20 in degrees.

Okay, lets begin

Approximately 41.81°

Explanation

Arcsin 14/20 is the angle whose sine is 0.7.

Since, sin 41.81° = 0.7(approx.), arcsin(14 ÷ 20) = 41.81°(approx.)

Well explained 👍

Problem 5

Verify arcsin 14/20 using the unit circle

Okay, lets begin

Approximately 41.81° or 0.7227 radians

Explanation

On the unit circle, the point (√(1 − 0.7²), 0.7) corresponds to sin θ = 0.7, so θ = 41.81° or 0.7227 radians (approx.), confirming arcsin(14 ÷ 20) = 41.81° or 0.7227 radians (approx.).

Well explained 👍

FAQs On Arcsin 14/20

1.How to find the value of arcsin 14/20?

Arcsin 14/20 approximately equals 41.81° or 0.7227 radians.

2.What are the conditions for arcsin?

The conditions for arcsin are:  the input must be between -1 and 1, and the output angle is always between (-90° and 90°) or (-π/2 and π/2 radians)

3.Why is it called arcsin?

It is called arcsin because it gives the angle whose sine equals a given number.

4.What is the law of arcsin?

The law of arcsin says that the time a random process (like Brownian motion) spends above zero follows an arcsine distribution.

This means it’s more likely to spend either very little or almost all the time above zero, rather than half.

5.What is the full form of arcsin?

The full form of arcsin, or inverse sine arcsin, is the function that gives the angle θ for a given ratio of opposite side to hypotenuse.

Important Glossary of Arcsin 14/20

  • Arcsin - Arcsin (arcsin) is the inverse sine function that gives the angle whose sine equals a given value, within (-π/2 to π/2).
  • Radians - A way to measure angles based on the arc length of a circle, where π radians = 180°.
  • Inverse Function - A function that reverses the effect of the original function, such as arcsin for sin.
  • Unit Circle - A circle with a radius of one, used to define trigonometric functions.
  • Principal Range - The set of output values (-90°, 90°) for arcsin, ensuring unique results.

Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.