根 90000000cos(wt)cos(wt+31.8)

解

根

90000000 cos (wt) cos (wt + 31.8)

t = \frac{π}{2 w} + \frac{2 πn}{w}, t = \frac{3 π}{2 w} + \frac{2 πn}{w}, t = \frac{π}{2 w} + \frac{6.28318 \dots n}{w} - \frac{31.8}{w}, t = \frac{6.28318 \dots n}{w} - \frac{27.08761 \dots}{w}

解答ステップ

90000000 cos (wt) cos (wt + 31.8)

根はx軸の切片である

(y = 0)

90000000 cos (wt) cos (wt + 31.8) = 0

各部分を別個に解く

cos (wt) = 0 or cos (wt + 31.8) = 0

cos (wt) = 0 : t = \frac{π}{2 w} + \frac{2 πn}{w}, t = \frac{3 π}{2 w} + \frac{2 πn}{w}; w \neq = 0

cos (wt + 31.8) = 0 : t = \frac{π}{2 w} + \frac{6.28318 \dots n}{w} - \frac{31.8}{w}, t = \frac{6.28318 \dots n}{w} - \frac{27.08761 \dots}{w}; w \neq = 0

すべての解を組み合わせる

t = \frac{π}{2 w} + \frac{2 πn}{w}, t = \frac{3 π}{2 w} + \frac{2 πn}{w}, t = \frac{π}{2 w} + \frac{6.28318 \dots n}{w} - \frac{31.8}{w}, t = \frac{6.28318 \dots n}{w} - \frac{27.08761 \dots}{w}