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112 LearnersLast updated on December 11, 2025
Arcsin 14/20
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.
Mistake 1
Confusing arcsin with sin
Always remember that arcsin returns the angle corresponding to a given sine value, not the sine itself.
For example, If sin θ = 0.7, then arcsin 0.7 = 41.81°(approx.) or 0.7227 radians, not 0.7.
Mistake 2
Ignoring the principal branch range
Always remember that arcsin results are restricted to the range( -π/2 and π/2) (or -90° and 90°)
For example, sin 41.81° = 0.7, and arcsin 0.7 = 41.81°(approx.) because it falls within the principal range.
Mistake 3
Forgetting radians and degrees conversion
Make it a habit to convert between radians and degrees to avoid errors.
For example, arcsin(14 ÷ 20) = 41.81°(approx) = 0.7227(approx) radians.
Mistake 4
Recognizing that different angles may satisfy the condition
Always remember that even though sine is periodic, only the angle within the principal range is valid.
For example, sin 318.19° = 0.7, but arcsin(14 ÷ 20) is still 41.81° because we consider only angles from -90° to 90°.
Mistake 5
Confusing points on the unit circle
Always picture the point (√(1 − 0.7²), 0.7) on the unit circle to find the correct angle.
For example, the coordinates \(√(1 − 0.7²), 0.7) correspond to θ = 41.81°(approx.) or 0.7227 radians.
Solved Examples on Arcsin 14/20
Problem 1
Find arcsin 14/20.
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).
Problem 2
If \(\sin \theta = 0.7\), find \(\theta\) using arcsin.
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.
Problem 3
Express arcsin 14/20 in radians.
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.)
Problem 4
Express arcsin 14/20 in degrees.
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.)
Problem 5
Verify arcsin 14/20 using the unit circle
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.).
FAQs On Arcsin 14/20
1.How to find the value of arcsin 14/20?
2.What are the conditions for arcsin?
3.Why is it called arcsin?
4.What is the law of arcsin?
5.What is the full form of arcsin?
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.
