The inverse sine function is represented as $f(x)=sin^{-1}x$. Here the -1 is not an exponent, it represents the inverse.The another name for $sin^{-1}x$ is arcsinx.

ask-math has already explains you about the sine graph. The domain for sine is $\frac{-\prod }{2}\leq x \leq \frac{\prod}{2}$. The sine inverse function is not one-to-one function so it is restricted sine function.

The another name for inverse sine function is :

To evaluate inverse sine functions remember that the following statement is equivalent.

In other words, when we evaluate sine inverse function we are asking what angle,θ, did we plug into the sine function (regular, not inverse!) to get x.

f(x)= sin(x) |
Domain $\frac{-\prod }{2}\leq x \leq \frac{\prod}{2}$ |
Range $-1\leq y \leq 1$ |

$f(x)=sin^{-1}x$ |
$-1\leq x \leq 1$ |
$\frac{-\prod }{2}\leq y \leq \frac{\prod}{2}$ |

In sine function, we know that $sin \Theta =\frac{opposite side }{hypotenuse}$

The inverse sine function $sin{-1}$ takes the ratio opposite/hypotenuse and gives the angle θ.

∴ θ = $sin^{-1}(\frac{opposite side }{hypotenuse})$

For example, $sin 30^{0} =\frac{1}{2}$

∴ θ = $sin^{-1}(\frac{1}{2})$

⇒ θ = $30^{0}$

y = $sin^{-1}(\frac{\sqrt{2}}{2})$

⇒ y = $45^{0}$ ( For the degree you can use a unit circle or calculator)

2) Evaluate f(x) = $sin^{-1}(\frac{\sqrt{3}}{2})$

y = $sin^{-1}(\frac{\sqrt{3}}{2})$

⇒ y = $60^{0}$

3) Find y, when sin(y) = 0.2384.

∴ y = $sin^{-1}(0.2384) $

⇒ y = $13.798^{0}

⇒ y = $13.8^{0}

4) Evaluate : f(x) = $sin^{-1}(sin(\frac{\prod }{4}))$

y = $sin^{-1}(sin(\frac{\prod }{4}))$

The value of $sin(\frac{\prod }{4}) = (\frac{\sqrt{2}}{2})$

∴ y = $sin^{-1}(\frac{\sqrt{2}}{2})$

∴ y = $45^{0}$

5) Evaluate f(x) = $sin^{-1}(1)$

y = $sin^{-1}(1)$

⇒ y = $90^{0}$

precalculus

Home

We at **ask-math **believe that educational material should be free for everyone. Please use the content of this website for in-depth understanding of the concepts. Additionally, we have created and posted videos on our youtube.

**We also offer One to One / Group Tutoring sessions / Homework help for Mathematics from Grade 4th to 12th for algebra, geometry, trigonometry, pre-calculus, and calculus for US, UK, Europe, South east Asia and UAE students.**

**Affiliations with Schools & Educational institutions are also welcome.**

Please reach out to us on [email protected] / Whatsapp +919998367796 / Skype id: anitagovilkar.abhijit

We will be happy to post videos as per your requirements also. Do write to us.

GMAT

GRE

1st Grade

2nd Grade

3rd Grade

4th Grade

5th Grade

6th Grade

7th grade math

8th grade math

9th grade math

10th grade math

11th grade math

12th grade math

Precalculus

Worksheets

Chapter wise Test

MCQ's

Math Dictionary

Graph Dictionary

Multiplicative tables

Math Teasers

NTSE

Chinese Numbers

CBSE Sample Papers