2020-수학-가형-홀수-7¶
문제¶
풀이¶
from sympy import *
x = Symbol("x")
domain = Interval.open(0, 2*pi)
[domain.contains(0), domain.contains(1), domain.contains(6), domain.contains(2*pi)]
[False, True, True, False]
soln = solveset(4*cos(x)**2 - 1, x, domain)
soln
\[\displaystyle \left\{\frac{\pi}{3}, \frac{2 \pi}{3}, \frac{4 \pi}{3}, \frac{5 \pi}{3}\right\}\]
ans = 0
for a in soln:
print([a,(sin(x)*cos(x)).subs(x,a)])
if (sin(x)*cos(x)).subs(x,a)<0:
ans += a
ans
[pi/3, sqrt(3)/4]
[2*pi/3, -sqrt(3)/4]
[4*pi/3, sqrt(3)/4]
[5*pi/3, -sqrt(3)/4]
\[\displaystyle \frac{7 \pi}{3}\]