- #1
zxh
- 8
- 0
Sry, noob, but i didn't find this anywhere.
No it's only a segment of the curve, but the graph of y=arcsin(x) would fit over y=-sin(x) if rotated 90° either way about the origin.zxh said:So the title would be true for -sin, viewed as a curve?
Jarle said:You can show this algebraically. If you are familiar with complex numbers, this is easy.
1) multiply x+i (-sin x) with e^(i*pi/2) to rotate it by 90 degrees.
2) reflect x+i(-sin x) over the curve y=x to invert it.
The arcsin function is the inverse of the sin function. When a function is rotated by 90°, its inverse is also rotated by 90° in the opposite direction. Therefore, arcsin sin rotated by 90° results in a function that is equivalent to the original sin function.
Rotating a function by 90° affects its inverse by also rotating it by 90° in the opposite direction. This is because the inverse of a function is essentially a reflection of the original function over the line y=x. Therefore, any transformation applied to the original function will also be applied to its inverse.
Rotating a function by 90° is a common mathematical operation used to transform functions and explore their properties. It can help to simplify complex functions, visualize relationships between functions and their inverses, and solve equations involving trigonometric functions.
Yes, arcsin sin can be rotated by any angle. However, rotating a function by an angle other than 90° may result in a different function with different properties. It is important to consider the specific angle being rotated and its effects on the function and its inverse.
The rotation of arcsin sin by 90° affects its graph by simply rotating it by 90° in the opposite direction. This means that the x and y coordinates of each point on the graph will switch places, resulting in a mirror image of the original graph over the line y=x. The shape of the graph will remain the same, but its orientation will change.