正弦
正弦的升维解释
- 边长为1 的平行四边形定义为单位平行四边形。
- 改变两边夹角，夹角的正弦等于单位平行四边形的面积。
params:
- {name: theta, value: 0.78, min: 0, max: 1.57, round: 0.01}
calcs:
angleDgree: (params.theta*180/3.14)
x2: (cos(params.theta))
y2: (sin(params.theta))
layout:
type: OneGraphPlusSidebar
def:
graph:
xAxis: { min: -0.2, max: 2}
yAxis: { min: -0.2, max: 2}
gridlines: true
objects:
- Point:
coordinates: [0, 0]
color: blue
label: A
- Point:
coordinates: [1, 0]
color: blue
label: B
- Point:
coordinates: [calcs.x2 + 1, calcs.y2]
color: blue
label: C
- Point:
coordinates: [calcs.x2, calcs.y2]
color: red
label: D
drag:
- directions: xy
param: theta
expression: atan2(drag.y,drag.x)
# 平行四边形的四条边
- Segment:
a: [0, 0]
b: [1, 0]
color: black
thickness: 2
- Segment:
a: [1, 0]
b: [calcs.x2 + 1, calcs.y2]
color: black
thickness: 2
- Segment:
a: [calcs.x2 + 1, calcs.y2]
b: [calcs.x2, calcs.y2]
color: black
thickness: 2
- Segment:
a: [calcs.x2, calcs.y2]
b: [0, 0]
color: black
thickness: 2
- AngleMarker:
measure: calcs.angleDgree
coordinates: [0,0]
sidebar:
controls:
- title: 平行四边形
description: "`
平行四边形的面积等于两边夹角的正弦值
`" sliders: - {param: theta, label: \theta} divs: - html: "`sin${calcs.angleDgree.toFixed(0)}$^{\\\\circ}$=${calcs.y2.toFixed(2)}`"
