・tan 15°...は、√の計算をします。
・私は、90°を超えるtan? を考えた事ありませんでした。180°を超える場合も。
Doc
The tangent function.
Returns the tangent of x (measured in radians).
https://docs.sympy.org/latest/modules/functions/elementary.html#sympy.functions.elementary.trigonometric.tan
sympyで(５°づつ。0°〜180°)
from sympy import *
pitch=5
for i in range(Integer(180/pitch)+1):
j=pitch*i
jstr=str(j).rjust(3, ' ')+"°"
myStr=str( tan(j*pi/180).simplify() )
if j==90:
myFlt='zoo'
else:
myFlt=str(float(tan(j*pi/180)))
if 'pi' in myStr:
print("#",jstr,15*" ",'{:<47}'.format(myStr)+myFlt)
else:
print("#",jstr ,'{:<63}'.format(myStr)+myFlt)
# 0° 0 0.0
# 5° tan(pi/36) 0.08748866352592401
# 10° tan(pi/18) 0.17632698070846498
# 15° 2 - sqrt(3) 0.2679491924311227
# 20° tan(pi/9) 0.36397023426620234
# 25° tan(5*pi/36) 0.4663076581549986
# 30° sqrt(3)/3 0.5773502691896257
# 35° tan(7*pi/36) 0.7002075382097098
# 40° tan(2*pi/9) 0.83909963117728
# 45° 1 1.0
# 50° tan(5*pi/18) 1.19175359259421
# 55° tan(11*pi/36) 1.4281480067421146
# 60° sqrt(3) 1.7320508075688772
# 65° tan(13*pi/36) 2.1445069205095586
# 70° tan(7*pi/18) 2.747477419454622
# 75° sqrt(3) + 2 3.732050807568877
# 80° tan(4*pi/9) 5.671281819617709
# 85° tan(17*pi/36) 11.430052302761343
# 90° zoo zoo
# 95° -(cos(pi/18) + 1)/sin(pi/18) -11.430052302761343
# 100° -tan(4*pi/9) -5.671281819617709
# 105° -2 - sqrt(3) -3.732050807568877
# 110° -1/tan(pi/9) -2.747477419454622
# 115° -1/cos(2*pi/9) - tan(2*pi/9) -2.1445069205095586
# 120° -sqrt(3) -1.7320508075688772
# 125° -1/cos(pi/9) - tan(pi/9) -1.4281480067421146
# 130° -1/cos(pi/18) - tan(pi/18) -1.19175359259421
# 135° -1 -1.0
# 140° -tan(2*pi/9) -0.83909963117728
# 145° -tan(7*pi/36) -0.7002075382097098
# 150° -sqrt(3)/3 -0.5773502691896257
# 155° -tan(5*pi/36) -0.4663076581549986
# 160° -tan(pi/9) -0.36397023426620234
# 165° -2 + sqrt(3) -0.2679491924311227
# 170° -tan(pi/18) -0.17632698070846498
# 175° -tan(pi/36) -0.08748866352592401
# 180° 0 0.0
sympyで(１°づつ。0°〜180°)
・√の出力の角度のみprint。
from sympy import *
pitch=1
for i in range(Integer(180/pitch)+1):
j=pitch*i
jstr=str(j).rjust(3, ' ')+"°"
myStr=str(tan(j*pi/180) )
if j==90:
print("#",jstr,'zoo')
elif 'pi' not in myStr:
print("#",jstr, tan(j*pi/180).simplify())
# 0° 0
# 3° (-sqrt(15) - sqrt(10 - 2*sqrt(5)) - sqrt(3) + 8)/(-sqrt(5) - 1 + sqrt(6)*sqrt(5 - sqrt(5)))
# 6° (-9 + sqrt(5) + sqrt(6*sqrt(5) + 30))/(-sqrt(2)*sqrt(sqrt(5) + 5) - sqrt(3) + sqrt(15))
# 9° -sqrt(5)*sqrt(2*sqrt(5) + 10)/4 - sqrt(2*sqrt(5) + 10)/4 + 1 + sqrt(5)
# 12° (-sqrt(1 - 2*sqrt(5)/5) + sqrt(3)/3)/(sqrt(3)*sqrt(1 - 2*sqrt(5)/5)/3 + 1)
# 15° 2 - sqrt(3)
# 18° sqrt(25 - 10*sqrt(5))/5
# 21° (-8 - sqrt(3) + sqrt(2*sqrt(5) + 10) + sqrt(15))/(-sqrt(6)*sqrt(sqrt(5) + 5) - 1 + sqrt(5))
# 24° (-sqrt(5 - 2*sqrt(5)) + sqrt(3))/(1 + sqrt(3)*sqrt(5 - 2*sqrt(5)))
# 27° -sqrt(5)*sqrt(10 - 2*sqrt(5))/4 - 1 + sqrt(10 - 2*sqrt(5))/4 + sqrt(5)
# 30° sqrt(3)/3
# 33° (-sqrt(15) - sqrt(3) + sqrt(10 - 2*sqrt(5)) + 8)/(1 + sqrt(5) + sqrt(6)*sqrt(5 - sqrt(5)))
# 36° sqrt(5 - 2*sqrt(5))
# 39° (-sqrt(2*sqrt(5) + 10) - sqrt(3) + sqrt(15) + 8)/(-1 + sqrt(5) + sqrt(6)*sqrt(sqrt(5) + 5))
# 42° (-sqrt(30 - 6*sqrt(5)) + sqrt(5) + 9)/(sqrt(3) + sqrt(2)*sqrt(5 - sqrt(5)) + sqrt(15))
# 45° 1
# 48° -(sqrt(3) + sqrt(2*sqrt(5) + 5))/(-sqrt(3)*sqrt(2*sqrt(5) + 5) + 1)
# 51° (-sqrt(15) + sqrt(3) + sqrt(2*sqrt(5) + 10) + 8)/(-1 + sqrt(5) + sqrt(6)*sqrt(sqrt(5) + 5))
# 54° sqrt(10*sqrt(5) + 25)/5
# 57° (-sqrt(10 - 2*sqrt(5)) + sqrt(3) + sqrt(15) + 8)/(1 + sqrt(5) + sqrt(6)*sqrt(5 - sqrt(5)))
# 60° sqrt(3)
# 63° -1 - sqrt(10 - 2*sqrt(5))/4 + sqrt(5)*sqrt(10 - 2*sqrt(5))/4 + sqrt(5)
# 66° (-sqrt(5) + sqrt(6*sqrt(5) + 30) + 9)/(-sqrt(3) + sqrt(2)*sqrt(sqrt(5) + 5) + sqrt(15))
# 69° (-8 - sqrt(15) - sqrt(2*sqrt(5) + 10) + sqrt(3))/(-sqrt(6)*sqrt(sqrt(5) + 5) - 1 + sqrt(5))
# 72° sqrt(2*sqrt(5) + 5)
# 75° sqrt(3) + 2
# 78° (sqrt(5) + sqrt(30 - 6*sqrt(5)) + 9)/(-sqrt(2)*sqrt(5 - sqrt(5)) + sqrt(3) + sqrt(15))
# 81° sqrt(2*sqrt(5) + 10)/4 + 1 + sqrt(5)*sqrt(2*sqrt(5) + 10)/4 + sqrt(5)
# 84° (sqrt(3)/3 + sqrt(2*sqrt(5)/5 + 1))/(-sqrt(3)*sqrt(2*sqrt(5)/5 + 1)/3 + 1)
# 87° (sqrt(3) + sqrt(10 - 2*sqrt(5)) + sqrt(15) + 8)/(-sqrt(5) - 1 + sqrt(6)*sqrt(5 - sqrt(5)))
# 90° zoo
# 93° (sqrt(10 - 2*sqrt(5)) + sqrt(3)*(1 + sqrt(5)) + 8)/(-sqrt(6)*sqrt(5 - sqrt(5)) + 1 + sqrt(5))
# 96° (sqrt(5 - 2*sqrt(5)) + sqrt(3))/(-sqrt(3)*sqrt(5 - 2*sqrt(5)) + 1)
# 99° -sqrt(5) - sqrt(5)*sqrt(2*sqrt(5) + 10)/4 - 1 - sqrt(2*sqrt(5) + 10)/4
# 102° (-9 - sqrt(30 - 6*sqrt(5)) - sqrt(5))/(-sqrt(2)*sqrt(5 - sqrt(5)) + sqrt(3) + sqrt(15))
# 105° -2 - sqrt(3)
# 108° -sqrt(2*sqrt(5) + 5)
# 111° (-sqrt(3) + sqrt(2*sqrt(5) + 10) + sqrt(15) + 8)/(-sqrt(6)*sqrt(sqrt(5) + 5) - 1 + sqrt(5))
# 114° (-9 - sqrt(6*sqrt(5) + 30) + sqrt(5))/(-sqrt(3) + sqrt(2)*sqrt(sqrt(5) + 5) + sqrt(15))
# 117° -sqrt(5) - sqrt(5)*sqrt(10 - 2*sqrt(5))/4 + sqrt(10 - 2*sqrt(5))/4 + 1
# 120° -sqrt(3)
# 123° (-8 - sqrt(15) - sqrt(3) + sqrt(10 - 2*sqrt(5)))/(1 + sqrt(5) + sqrt(6)*sqrt(5 - sqrt(5)))
# 126° -sqrt(10*sqrt(5) + 25)/5
# 129° (-8 - sqrt(2*sqrt(5) + 10) - sqrt(3) + sqrt(15))/(-1 + sqrt(5) + sqrt(6)*sqrt(sqrt(5) + 5))
# 132° -(sqrt(1 - 2*sqrt(5)/5) + sqrt(3)/3)/(-sqrt(3)*sqrt(1 - 2*sqrt(5)/5)/3 + 1)
# 135° -1
# 138° (-9 - sqrt(5) + sqrt(30 - 6*sqrt(5)))/(sqrt(3) + sqrt(2)*sqrt(5 - sqrt(5)) + sqrt(15))
# 141° (-8 - sqrt(15) + sqrt(3) + sqrt(2*sqrt(5) + 10))/(-1 + sqrt(5) + sqrt(6)*sqrt(sqrt(5) + 5))
# 144° -sqrt(5 - 2*sqrt(5))
# 147° (-8 - sqrt(10 - 2*sqrt(5)) + sqrt(3) + sqrt(15))/(1 + sqrt(5) + sqrt(6)*sqrt(5 - sqrt(5)))
# 150° -sqrt(3)/3
# 153° -sqrt(5) - sqrt(10 - 2*sqrt(5))/4 + 1 + sqrt(5)*sqrt(10 - 2*sqrt(5))/4
# 156° (-sqrt(2*sqrt(5)/5 + 1) + sqrt(3)/3)/(sqrt(3)*sqrt(2*sqrt(5)/5 + 1)/3 + 1)
# 159° (-sqrt(15) - sqrt(2*sqrt(5) + 10) + sqrt(3) + 8)/(-sqrt(6)*sqrt(sqrt(5) + 5) - 1 + sqrt(5))
# 162° -sqrt(25 - 10*sqrt(5))/5
# 165° -2 + sqrt(3)
# 168° (-sqrt(2*sqrt(5) + 5) + sqrt(3))/(1 + sqrt(3)*sqrt(2*sqrt(5) + 5))
# 171° -sqrt(5) - 1 + sqrt(2*sqrt(5) + 10)/4 + sqrt(5)*sqrt(2*sqrt(5) + 10)/4
# 174° (-sqrt(6*sqrt(5) + 30) - sqrt(5) + 9)/(-sqrt(2)*sqrt(sqrt(5) + 5) - sqrt(3) + sqrt(15))
# 177° (-8 + sqrt(3) + sqrt(10 - 2*sqrt(5)) + sqrt(15))/(-sqrt(5) - 1 + sqrt(6)*sqrt(5 - sqrt(5)))
# 180° 0
参考
＞Important Angles
勉強中