Solve (2 + sqrt3) cosθ = 1-sinθ?

대답:

# rarrx = (6n-1) * (pi / 3) #

# rarrx = (4n + 1) pi / 2 # 어디에 # nrarrZ #

설명:

#rarr (2 + sqrt (3)) cosx = 1-sinx #

# rarrtan75 ^ @ * cosx + sinx = 1 #

#rarr (sin75 ^ @ * cosx) / (cos75 ^ @) + sinx = 1 #

(90 ^ @ - 15 ^ @) = sin15 ^ @ # cos = sin75 ^ @ + cosx * sin75 ^ @ = cos75 ^ @ =

#rarrsin (x + 75 ^ @) - sin15 ^ @ = 0 #

(x + 75 ^ @ + 15 ^ @) / 2) = 0 #

#rarrsin ((x + 60 ^ @) / 2) * cos ((x + 90 ^ @) / 2) = 0 #

어느 한 쪽 #rarrsin ((x + 60 ^ @) / 2) = 0 #

#rarr (x + 60 ^ @) / 2 = npi #

# rarrx = 2npi-60 ^ @ = 2npi-pi / 3 = (6n-1) * (pi / 3) #

또는, #cos ((x + 90 ^ @) / 2) = 0 #

#rarr (x + 90 ^ @) / 2 = (2n + 1) pi / 2 #

# rarrx = 2 * (2n + 1) pi / 2-pi / 2 = (4n + 1) pi / 2 #

대답:

만약, # costheta = 0 => sintheta = 1 => theta = (4k + 1) pi / 2, kinZ #

# theta = 2kpi-pi / 3, kinZ #,

설명:

# (2 + sqrt3) costheta = 1-sintheta #

#andcostheta! = 0 #, 양쪽을 # costheta #

# 2 + sqrt3 = sectheta-tantheta => sectheta-tantheta = 2 + sqrt3 ~ (I) #

#: 1 / (섹터 - 탄 체타) = 1 / (2 + sqrt3) #1 / (2 + sqrt3) * (2-sqrt3) / (2-sqrt3) # (sec ^ 2theta-tan ^ 2theta) / (sectheta-tantheta)

# => sectheta + tantheta = 2-sqrt3 ~ (II) #

첨가 # (I) 및 (II) #, 우리는 얻는다.# 2sectheta = 4 => sectheta = 2 #

#color (빨강) (costheta = 1 / 2> 0) #, 주어진 equn으로부터.

# costheta = 1 / 2 => (2 + sqrt3) (1/2) = 1-sintheta ## => 1 + sqrt (3) / 2 = 1-sintheta => 색상 (적색) (신테 타 = -sqrt (3) / 2 <0) #

# theta = 2kpi-pi / 3, kinZ #,………. # (IV ^ (th) #사분면)