[Triangle construction] Part of a proof for sin(x)sin(y). #manim #triangle #geometry #trigonometry #animation

20241017_sinxsiny.py

from manim import *

class sinxsiny(Scene):
    def construct(self):
        O = Dot([-3,-3.0,0], color=YELLOW, radius=0.05)
        A = Dot([3,-3.0,0], color=YELLOW, radius=0.05)
        lbl_O = MathTex(r"O").next_to(O,LEFT)
        lbl_A = MathTex(r"A").next_to(A,RIGHT)
        x = 35*DEGREES
        y = 20*DEGREES
        OA = Line(O.get_center(),A.get_center())
        self.play(Create(OA))
        self.play(Create(O),Write(lbl_O))
        self.play(Create(A),Write(lbl_A))
        OB = Line(O.get_center(),A.get_center())
        B = always_redraw(lambda:
            Dot(OB.get_end(), color=YELLOW, radius=0.05)
        )
        lbl_B = always_redraw(lambda:
            MathTex(r"B").next_to(B.get_center(),RIGHT)
        )
        AB = always_redraw(lambda:
            Line(A.get_center(),B.get_center())
        )
        ang_x = always_redraw(lambda:
            Arc(radius=0.5, start_angle=0, angle=OB.get_angle()).shift(O.get_center())
        )
        self.play(Create(OB),Create(AB),Create(ang_x))
        self.play(Create(B),Write(lbl_B))
        self.play(
            OB.animate.rotate(angle=x,about_point=O.get_center()).scale(1/np.cos(x),about_point=O.get_center())
        )
        lbl_x = MathTex(r"x").rotate(-x/2).shift(0.7*RIGHT).rotate(x/2,about_point=ORIGIN).shift(O.get_center())
        self.play(Write(lbl_x))
        dummy = OB.copy().rotate(angle=-x,about_point=O.get_center())
        OC = dummy.copy()
        C = always_redraw(lambda:
            Dot(OC.get_end(), color=YELLOW, radius=0.05)
        )
        lbl_C = always_redraw(lambda:
            MathTex(r"C").next_to(C.get_center(),RIGHT)
        )
        BC = always_redraw(lambda:
            Line(OC.get_end(),dummy.get_end())
        )
        ang_y = always_redraw(lambda:
            Arc(radius=1, start_angle=dummy.get_angle(), angle=OC.get_angle()-dummy.get_angle()).shift(O.get_center())
        )
        self.play(
            Create(dummy),Create(OC),Create(BC),
            Write(lbl_C),Create(C),
            Create(ang_y)
        )
        self.play(
            OC.animate.rotate(angle=y,about_point=O.get_center()).scale(1/np.cos(y),about_point=O.get_center())
        )
        lbl_y = always_redraw(lambda:
            MathTex(r"y").rotate(-dummy.get_angle()-x/2).shift(1.2*RIGHT).rotate(+dummy.get_angle()+y/2,about_point=ORIGIN).shift(O.get_center())
        )
        self.play(Write(lbl_y))
        self.wait()
        self.play(
            Rotate(
                VGroup(dummy,OC,BC),
                angle=x,
                about_point=O.get_center()
            )
        )
        E = Dot(point=[C.get_center()[0],A.get_center()[1],0], color=YELLOW, radius=0.05)
        lbl_E = MathTex(r"E").next_to(E,DOWN,buff=0.05)
        D = Dot(point=[C.get_center()[0],B.get_center()[1],0], color=YELLOW, radius=0.05)
        lbl_D = MathTex(r"D").next_to(D,LEFT)
        CE = Line(C.get_center(),E.get_center())
        BD = Line(B.get_center(),D.get_center())
        self.play(Create(CE))
        self.play(Create(E),Write(lbl_E))
        self.play(Create(BD))
        self.play(Create(D),Write(lbl_D))
        ang_x.suspend_updating()
        lbl_x.suspend_updating()
        ang_y.suspend_updating()
        lbl_y.suspend_updating()
        ang_x2 = VGroup(ang_x.copy(),lbl_x.copy())
        self.play(
            ang_x2.animate.shift(C.get_center()-O.get_center())
        )
        self.play(
            Rotate(ang_x2, -PI/2, about_point=C.get_center())
        )
        ang_x3 = ang_x2.copy()
        self.play(
            ang_x3.animate.shift(B.get_center()-C.get_center())
        )
        self.play(
            Rotate(ang_x3, -PI/2, about_point=B.get_center())
        )
        self.wait()

readme.md