2020-수학-가형-홀수-9¶
문제¶
풀이¶
from sympy import *
t = symbols("t")
x = t+sin(t)*cos(t)
y = tan(t)
speed_sq = diff(x,t)**2 + diff(y,t)**2
speed_sq
\[\displaystyle \left(\tan^{2}{\left(t \right)} + 1\right)^{2} + \left(- \sin^{2}{\left(t \right)} + \cos^{2}{\left(t \right)} + 1\right)^{2}\]
speed_sq = simplify(speed_sq)
speed_sq
\[\displaystyle 4 \cos^{4}{\left(t \right)} + \frac{1}{\cos^{4}{\left(t \right)}}\]
simplify(diff(speed_sq,t))
\[\displaystyle \frac{4 \left(1 - 4 \cos^{8}{\left(t \right)}\right) \sin{\left(t \right)}}{\cos^{5}{\left(t \right)}}\]
solveset(1-4*cos(t)**8, cos(t)**4, Interval(0,1))
\[\displaystyle \left\{\frac{1}{2}\right\}\]
v = sqrt(speed_sq)
c4 = Symbol('c4')
expr = v.subs(cos(t)**4,c4)
expr.subs(c4,1/2)
\[\displaystyle 2.0\]