The range of arcsiny is [-π/2, π/2]. When x is between π/2 and π, π-x is between 0 and π/2, and y=sinx=sin(π-x), then π-x=siny?
The volume of the Y=sinx rotating body around the y axis is solved as follows:
Extended data
Sine, a mathematical term, in a right triangle, the ratio of the opposite side to the hypotenuse of any acute angle ∠A is called sine of ∠A, which is abbreviated from the English word sine, that is, the opposite side/hypotenuse of Sina = ∠ A.
Generally speaking, in rectangular coordinate system, given the unit circle, for any angle α, the vertex of the angle α coincides with the origin, the starting edge coincides with the non-negative semi-axis of the X axis, and the ending edge intersects with the unit circle at point P(u, v), so the ordinate V of the point P is called the sine function of the angle α, and it is recorded as v=sinα. Usually, we use X to represent the independent variable, that is, X represents the size of the angle and Y represents the function value, so we define the trigonometric function y=sin x at any angle, and its definition domain is all real numbers, with the value range of [- 1, 1].
Sine function correlation formula:
Sum of squares relation
(sinα)^2 +(cosα)^2= 1
Product relationship
Sinα = tanα × cosα (that is, sinα/cosα = tanα)
Cosα = cotα × sinα (that is, cosα/sinα = cotα).
Tanα = sinα × secα (that is, tanα/sinα = secα).
Reciprocal relationship
tanα × cotα = 1
sinα × cscα = 1
cosα × secα = 1
Relationship of quotient
sinα / cosα = tanα = secα / cscα
Sum angle formula
sin ( α β ) = sinα cosβ cosα sinβ
sin(α+β+γ)= sinαcosβcosγ+cosαsinβcosγ+cosαcosβsinγ-sinαsinβsinγ
cos ( α β ) = cosα cosβ？ Octagonal β-Octagonal α
tan ( α β ) = ( tanα tanβ ) / ( 1？ tanα tanβ)
Double-angle and half-angle formulas
sin ( 2α ) = 2sinα cosα = 2 / ( tanα + cosα)
sin(3α)= 3 sinα-4 sin & amp； sup3(α ) = 4sinα sin ( 60 + α ) sin ( 60 - α)
sin ( α / 2 ) = √( ( 1 - cosα ) / 2)
Derived from Taylor series
Sinks = [East (9)-East (-9)]/(2i)
series expansion
sin x = x - x3 / 3！ + x5 / 5！ -...(- 1)k- 1 * 2k- 1/(2k- 1)！ +...(-∞& lt； x & lt∞ )
derivant
(sinx ) ' = cosx
(cosx)' =-Sinks
References:
Baidu encyclopedia sine function