[从头学数学] 第162节 锐角三角函数
剧情提要：
[机器小伟]在[project师阿伟]的陪同下进入了筑基后期的修炼，
这次要修炼的目标是[锐角三角函数]。
正剧開始：
星历2016年04月05日 10:20:54, 银河系厄尔斯星球中华帝国江南行省。
这样就能够非常快得到全部结果：
[机器小伟]在[project师阿伟]的陪同下进入了筑基后期的修炼，
这次要修炼的目标是[锐角三角函数]。
正剧開始：
星历2016年04月05日 10:20:54, 银河系厄尔斯星球中华帝国江南行省。
[project师阿伟]正在和[机器小伟]一起研究[锐角三角函数]。
这座塔真的非常壮观，不知如今还是否同意游客上去观光。
<span style="font-size:18px;"> if (1) {
config.setSector(1,1,1,1);
var r = 20;
config.graphPaper2D(0, 0, r);
config.axis2D(0, 0, 180);
//绘制三角形
var triangle = new Triangle();
var array = triangle.know2edges([10, 6], -90);
var scale = r;
shape.angleDraw([].concat(array), 'red', scale, 'ABC');
//求角的三角函数值
var angle = 36.87 / 180*Math.PI;
var sinA = Math.sin(angle), cosA = Math.cos(angle), tanA = Math.tan(angle);
//打印结果
var x = -200, y = -170;
var result = [];
result.push(['sinA = ', sinA]);
result.push(['cosA = ', cosA]);
result.push(['tanA = ', tanA]);
for (var i = 0; i < 3; i++) {
plot.fillText(result[i][0]+result[i][1].toFixed(3), x, y, 100);
y += 30;
}
}</span>
<span style="font-size:18px;">//第1题
if (1) {
config.setSector(1,1,1,1);
var r = 20;
config.graphPaper2D(0, 0, r);
config.axis2D(0, 0, 180);
//绘制三角形
var triangle = new Triangle();
var array = triangle.know2edges([13, 12], -90);
var scale = r;
shape.angleDraw([].concat(array), 'red', scale, 'BAC');
//求角的三角函数值
var angle = 22.62 / 180*Math.PI;
var sinA = Math.sin(angle), cosA = Math.cos(angle), tanA = Math.tan(angle);
//打印结果
var x = -200, y = -170;
var result = [];
result.push(['sinA = ', sinA]);
result.push(['cosA = ', cosA]);
result.push(['tanA = ', tanA]);
for (var i = 0; i < 3; i++) {
plot.fillText(result[i][0]+result[i][1].toFixed(3), x, y, 100);
y += 30;
}
//求角的三角函数值
angle = Math.PI/2- angle;
sinA = Math.sin(angle);
cosA = Math.cos(angle);
tanA = Math.tan(angle);
//打印结果
x = -200, y = 30;
result = [];
result.push(['sinB = ', sinA]);
result.push(['cosB = ', cosA]);
result.push(['tanB = ', tanA]);
for (var i = 0; i < 3; i++) {
plot.fillText(result[i][0]+result[i][1].toFixed(3), x, y, 100);
y += 30;
}
}
</span>
<span style="font-size:18px;"> if (1) {
config.setSector(1,1,1,1);
var r = 20;
config.graphPaper2D(0, 0, r);
config.axis2D(0, 0, 180);
//绘制三角形
var triangle = new Triangle();
var array = triangle.know2edges([2, 3], 90);
var scale = 3*r;
shape.angleDraw([].concat(array), 'red', scale, 'ACB');
//求角的三角函数值
var angle = 56.31 / 180*Math.PI;
var sinA = Math.sin(angle), cosA = Math.cos(angle), tanA = Math.tan(angle);
//打印结果
var x = -200, y = -170;
var result = [];
result.push(['sinA = ', sinA]);
result.push(['cosA = ', cosA]);
result.push(['tanA = ', tanA]);
for (var i = 0; i < 3; i++) {
plot.fillText(result[i][0]+result[i][1].toFixed(3), x, y, 100);
y += 30;
}
//求角的三角函数值
angle = Math.PI/2- angle;
sinA = Math.sin(angle);
cosA = Math.cos(angle);
tanA = Math.tan(angle);
//打印结果
x = -200, y = 30;
result = [];
result.push(['sinB = ', sinA]);
result.push(['cosB = ', cosA]);
result.push(['tanB = ', tanA]);
for (var i = 0; i < 3; i++) {
plot.fillText(result[i][0]+result[i][1].toFixed(3), x, y, 100);
y += 30;
}
}</span>
<span style="font-size:18px;">>>> import math; >>> math.sin(18) -0.750987246771676 >>> math.sin(18/180*math.pi) 0.3090169943749474 >>> math.tan(30.6/180*math.pi) 0.5913983513994712</span>
<span style="font-size:18px;">>>> math.asin(0.5018); 0.5256784866432485 >>> _*180/math.pi 30.119158665482352 >>> a = _; >>> (a-math.floor(a))*60; 7.149519928941146 >>> b = _; >>> (b-math.floor(b))*60; 8.971195736468758</span>
为了方便以后的计算。阿伟制作了一件法器：
<span style="font-size:18px;">###
# @usage 三角函数调用封装
# @author mw
# @date 2016年04月05日 星期二 09:36:50
# @param
# @return
#
###
def triFun():
#须要计算的任务
#输入量为角度制，依次为度。分，秒
#可输出显示度、分、秒的表达式
#用于计算锐角三角函数
#对于角度变换，还没有经过測试
#以后可扩展加入其他多种数学函数
task = [
['sin', 20],
['cos', 70],
['sin', 35],
['cos', 55],
['sin', 15, 32],
['cos', 74, 28],
['tan', 3, 8],
['tan', 80, 25, 43],
['asin', 0.6275],
['asin', 0.0547],
['acos', 0.6252],
['acos', 0.1659],
['atan', 4.8425],
['atan', 0.8816],
['sin', 18],
['tan', 30, 36],
['asin', 0.5018]
];
size = len(task);
result = [];
import math;
for i in range(size):
if task[i][0] == 'sin' or task[i][0] == 'cos' or task[i][0] == 'tan' \
or task[i][0] == 'cot':
size_1 = len(task[i]);
angle = 0;
if size_1 == 2:
angle = task[i][1];
elif size_1 == 3:
angle = task[i][1]+task[i][2]/60;
elif size_1 == 4:
angle = task[i][1]+task[i][2]/60+task[i][3]/3600;
angle = angle/180*math.pi;
if task[i][0] == 'sin':
s = '';
if size_1 == 2:
s = task[i][0]+str(task[i][1])+'°';
elif size_1 == 3:
s = task[i][0]+str(task[i][1])+'°'+str(task[i][2])+'\'';
elif size_1 == 4:
s = task[i][0]+str(task[i][1])+'°'+str(task[i][2])+'\''+str(task[i][3])+'″';
s += ' = ';
s += str(round(math.sin(angle), 3));
s += '\n';
result.append(s);
elif task[i][0] == 'cos':
s = '';
if size_1 == 2:
s = task[i][0]+str(task[i][1])+'°';
elif size_1 == 3:
s = task[i][0]+str(task[i][1])+'°'+str(task[i][2])+'\'';
elif size_1 == 4:
s = task[i][0]+str(task[i][1])+'°'+str(task[i][2])+'\''+str(task[i][3])+'″';
s += ' = ';
s += str(round(math.cos(angle), 3));
s += '\n';
result.append(s);
elif task[i][0] == 'tan':
s = '';
if size_1 == 2:
s = task[i][0]+str(task[i][1])+'°';
elif size_1 == 3:
s = task[i][0]+str(task[i][1])+'°'+str(task[i][2])+'\'';
elif size_1 == 4:
s = task[i][0]+str(task[i][1])+'°'+str(task[i][2])+'\''+str(task[i][3])+'″';
s += ' = ';
s += str(round(math.tan(angle), 3));
s += '\n';
result.append(s);
elif task[i][0] == 'cot':
s = '';
if size_1 == 2:
s = task[i][0]+str(task[i][1])+'°';
elif size_1 == 3:
s = task[i][0]+str(task[i][1])+'°'+str(task[i][2])+'\'';
elif size_1 == 4:
s = task[i][0]+str(task[i][1])+'°'+str(task[i][2])+'\''+str(task[i][3])+'″';
s += ' = ';
s += str(round(1/math.tan(angle), 3));
s += '\n';
result.append(s);
else:
if task[i][0] == 'asin':
s = '';
s = task[i][0]+str(task[i][1])+' = ';
res = math.asin(task[i][1])/math.pi*180;
if res < 0:
s += '-';
absres = abs(res);
s += str(math.floor(absres))+'°'+str(math.floor(absres*60)%60)+'\''+str(round(absres*3600)%60)+'″';
s += '\n';
result.append(s);
elif task[i][0] == 'acos':
s = '';
s = task[i][0]+str(task[i][1])+' = ';
res = math.acos(task[i][1])/math.pi*180;
if res < 0:
s += '-';
absres = abs(res);
s += str(math.floor(absres))+'°'+str(math.floor(absres*60)%60)+'\''+str(round(absres*3600)%60)+'″';
s += '\n';
result.append(s);
elif task[i][0] == 'atan':
s = '';
s = task[i][0]+str(task[i][1])+' = ';
res = math.atan(task[i][1])/math.pi*180;
if res < 0:
s += '-';
absres = abs(res);
s += str(math.floor(absres))+'°'+str(math.floor(absres*60)%60)+'\''+str(round(absres*3600)%60)+'″';
s += '\n';
result.append(s);
elif task[i][0] == 'acot':
s = '';
s = task[i][0]+str(task[i][1])+' = ';
res = 90-math.atan(task[i][1])/math.pi*180;
if res < 0:
s += '-';
absres = abs(res);
s += str(math.floor(absres))+'°'+str(math.floor(absres*60)%60)+'\''+str(round(absres*3600)%60)+'″';
s += '\n';
result.append(s);
else:
pass;
size = len(result);
for i in range(size):
print(result[i]);
if __name__ == '__main__':
triFun();
</span>这样就能够非常快得到全部结果：
<span style="font-size:18px;">>>> sin20° = 0.342 cos70° = 0.342 sin35° = 0.574 cos55° = 0.574 sin15°32' = 0.268 cos74°28' = 0.268 tan3°8' = 0.055 tan80°25'43″ = 5.93 asin0.6275 = 38°51'57″ asin0.0547 = 3°8'8″ acos0.6252 = 51°18'11″ acos0.1659 = 80°27'2″ atan4.8425 = 78°19'56″ atan0.8816 = 41°23'58″ sin18° = 0.309 tan30°36' = 0.591 asin0.5018 = 30°7'9″</span>
<span style="font-size:18px;">//例1
if (1) {
config.setSector(1,1,1,1);
var r = 20;
config.graphPaper2D(0, 0, r);
config.axis2D(0, 0, 180);
//绘制三角形
var triangle = new Triangle();
var array = triangle.know2edges([Math.sqrt(6), Math.sqrt(2)], 90);
var scale = 3*r;
shape.angleDraw([].concat(array), 'red', scale, 'BCA');
//求角的三角函数值
var angle = 60 / 180*Math.PI;
var sinA = Math.sin(angle), cosA = Math.cos(angle), tanA = Math.tan(angle);
//打印结果
var x = -200, y = -170;
var result = [];
result.push(['sinA = ', sinA]);
result.push(['cosA = ', cosA]);
result.push(['tanA = ', tanA]);
for (var i = 0; i < 3; i++) {
plot.fillText(result[i][0]+result[i][1].toFixed(3), x, y, 100);
y += 30;
}
//求角的三角函数值
angle = Math.PI/2- angle;
sinA = Math.sin(angle);
cosA = Math.cos(angle);
tanA = Math.tan(angle);
//打印结果
x = -200, y = 30;
result = [];
result.push(['sinB = ', sinA]);
result.push(['cosB = ', cosA]);
result.push(['tanB = ', tanA]);
for (var i = 0; i < 3; i++) {
plot.fillText(result[i][0]+result[i][1].toFixed(3), x, y, 100);
y += 30;
}
}</span>
<span style="font-size:18px;">//例2
if (1) {
config.setSector(1,1,1,1);
var r = 20;
config.graphPaper2D(0, 0, r);
config.axis2D(0, 0, 180);
//绘制三角形
var triangle = new Triangle();
//此处两角分别为B, A，即第三、一两顶点。边则是AC， 即一、二两顶点
var array = triangle.know2angles([35, 55], 20);
var scale = r/4;
shape.angleDraw([].concat(array), 'red', scale, 'ACB');
//求角的三角函数值
var angle = 55 / 180*Math.PI;
var sinA = Math.sin(angle), cosA = Math.cos(angle), tanA = Math.tan(angle);
//打印结果
var x = -200, y = -170;
var result = [];
result.push(['sinA = ', sinA]);
result.push(['cosA = ', cosA]);
result.push(['tanA = ', tanA]);
for (var i = 0; i < 3; i++) {
plot.fillText(result[i][0]+result[i][1].toFixed(3), x, y, 100);
y += 30;
}
//求角的三角函数值
angle = Math.PI/2- angle;
sinA = Math.sin(angle);
cosA = Math.cos(angle);
tanA = Math.tan(angle);
//打印结果
x = -200, y = 30;
result = [];
result.push(['sinB = ', sinA]);
result.push(['cosB = ', cosA]);
result.push(['tanB = ', tanA]);
for (var i = 0; i < 3; i++) {
plot.fillText(result[i][0]+result[i][1].toFixed(3), x, y, 100);
y += 30;
}
}
</span>
<span style="font-size:18px;">//神舟飞船
if (1) {
config.setSector(1,1,1,1);
var r = 20;
config.graphPaper2D(0, 0, r);
config.axis2D(0, 0, 180);
//绘制三角形
var triangle = new Triangle();
//此处两边分别为FO，即第一二两顶点，OQ， 即二三两顶点，直角为Q
var array = triangle.know2edges([6400+343, 6400], -90);
var scale = 0.035;
shape.angleDraw([].concat(array), 'red', scale, 'FOQ');
//求角的三角函数值
var angle = 18.35 / 180*Math.PI;
var sinA = Math.sin(angle), cosA = Math.cos(angle), tanA = Math.tan(angle);
//打印结果
var x = -200, y = -170;
var result = [];
result.push(['sinA = ', sinA]);
result.push(['cosA = ', cosA]);
result.push(['tanA = ', tanA]);
for (var i = 0; i < 3; i++) {
plot.fillText(result[i][0]+result[i][1].toFixed(3), x, y, 100);
y += 30;
}
//求角的三角函数值
angle = Math.PI/2- angle;
sinA = Math.sin(angle);
cosA = Math.cos(angle);
tanA = Math.tan(angle);
//打印结果
x = -200, y = 30;
result = [];
result.push(['sinB = ', sinA]);
result.push(['cosB = ', cosA]);
result.push(['tanB = ', tanA]);
for (var i = 0; i < 3; i++) {
plot.fillText(result[i][0]+result[i][1].toFixed(3), x, y, 100);
y += 30;
}
y += 50;
plot.fillText('A => O , B => Q', x, y, 150);
}
>>> 18.35/180*3.142*6400
2049.9804444444444</span>
本节到此结束。欲知后事怎样。请看下回分解。
posted on 2017-07-29 15:48 gavanwanggw 阅读(443) 评论(0) 编辑 收藏 举报
