# Why is the inverse sine restricted?

## Why is the inverse sine restricted?

A restricted domain gives an inverse function because the graph is one to one and able to pass the horizontal line test. – The restricted sine function passes the horizontal line test, therefore it is one to one – Each range value (-1 to 1) is within the limited domain (-π/2, π/2).

## Why is the inverse of sin sin 1?

The inverse sin of 1, ie sin-1 (1) is a very special value for the inverse sine function. Remember that sin-1(x) will give you the angle whose sine is x . Therefore, sin-1 (1) = the angle whose sine is 1.

What is the value of sin inverse 1?

90°
The inverse of any trigonometric function is equal to an angle. We know that the value of sin-11 is 90°.

What is the inverse of sine called?

The inverse sine function (also called arcsine) is the inverse of sine function. Since sine of an angle (sine function) is equal to ratio of opposite side and hypotenuse, thus sine inverse of same ratio will give the measure of the angle.

### What is tan90 value?

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The exact value of tan 90 is infinity or undefined.

### Is Arcsin the same as sin 1?

It represents the inverse of the sine function. Recall f(x) and f-1(x). sin-1x means the same as arcsin x, i.e., the arc whose sine is x.

Does sin and sin-1 cancel out?

The arcsine function is the inverse function for the sine function on the interval . So they “cancel” each other under composition of functions, as follows. The notation for inverse functions, f-1(x) is just that: notation, a shorthand way of writing the inverse of a function f.

Is arcsin xx a sin?

By definition, arcsin:[−1,1]⟶[−π2,π2] is the inverse of the restriction to [−π2,π2] of the sine function. Therefore, for each x∈[−π2,π2] we have arcsin(sin(x))=x because that’s part of the definition of inverse functions.

## What is the formula for sin 1?

Table of Inverse Trigonometric Functions

Function Name Notation Range
Arcsine or inverse sine y = sin-1(x) − π/2 ≤ y ≤ π/2 -90°≤ y ≤ 90°
Arccosine or inverse cosine y=cos-1(x) 0 ≤ y ≤ π 0° ≤ y ≤ 180°
Arctangent or Inverse tangent y=tan-1(x) − π/2 < y < π/2 -90°< y < 90°
Arccotangent or Inverse Cot y=cot-1(x) 0 < y < π 0° < y < 180°

## What is the value of sin inverse 1 2?

-π/6
Therefore, principal value of sin-1(-1/2) = -π/6.

What is reciprocal of sin?

The cosecant is the reciprocal of the sine. It is the ratio of the hypotenuse to the side opposite a given angle in a right triangle.

How to solve the equation sin ( x ) 1 / 2?

Solve for? sin (x)=1/2. sin(x) = 1 2 sin ( x) = 1 2. Take the inverse sine of both sides of the equation to extract x x from inside the sine. x = arcsin(1 2) x = arcsin ( 1 2) The exact value of arcsin(1 2) arcsin ( 1 2) is π 6 π 6. x = π 6 x = π 6. The sine function is positive in the first and second quadrants.

### Which is the correct value for sin ( x )?

Take the inverse sine of both sides of the equation to extract x x from inside the sine. The exact value of arcsin(1 2) arcsin ( 1 2) is π 6 π 6. The sine function is positive in the first and second quadrants.

### How do you find inverse sin ( 1 / 2 )?

Using the ASTC rule, you know that for sin to be positive it has to be in Quadrant 1 and 2. But since this is a negative it has to be the complete opposite! So Quadrant 3 and 4 is where sin will be negative. In Quadrant 3, from the ASTC rule, take 180° + ∝ ⇒ ∝ being the answer you just got aka 30°!

Why is my sin not working in Python?

I’m not getting the results I expected, although after messing around with it I got close but it wasn’t quite right. Could someone please tell me what I’m doin wrong.