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人気のある三角関数 >

sec^2(θ)tan(θ)=2tan(θ),0<= θ<= 360

解

sec^{2} (θ) tan (θ) = 2 tan (θ), 0^{\circ} \leq θ \leq 36 0^{\circ}

解

θ = 0, θ = 18 0^{\circ}, θ = 36 0^{\circ}, θ = 13 5^{\circ}, θ = 22 5^{\circ}, θ = 4 5^{\circ}, θ = 31 5^{\circ}

+1

ラジアン

θ = 0, θ = π, θ = 2 π, θ = \frac{3 π}{4}, θ = \frac{5 π}{4}, θ = \frac{π}{4}, θ = \frac{7 π}{4}

解答ステップ

sec^{2} (θ) tan (θ) = 2 tan (θ), 0^{\circ} \leq θ \leq 36 0^{\circ}

両辺から

2 tan (θ)

を引く

sec^{2} (θ) tan (θ) - 2 tan (θ) = 0

因数

sec^{2} (θ) tan (θ) - 2 tan (θ) : tan (θ) (sec (θ) + 2) (sec (θ) - 2)

sec^{2} (θ) tan (θ) - 2 tan (θ)

共通項をくくり出す

tan (θ)

= tan (θ) (sec^{2} (θ) - 2)

因数

sec^{2} (θ) - 2 : (sec (θ) + 2) (sec (θ) - 2)

sec^{2} (θ) - 2

累乗根の規則を適用する:

a = (a)^{2}

2 = (2)^{2}

= sec^{2} (θ) - (2)^{2}

2乗の差の公式を適用する:

x^{2} - y^{2} = (x + y) (x - y)

sec^{2} (θ) - (2)^{2} = (sec (θ) + 2) (sec (θ) - 2)

= (sec (θ) + 2) (sec (θ) - 2)

= tan (θ) (sec (θ) + 2) (sec (θ) - 2)

tan (θ) (sec (θ) + 2) (sec (θ) - 2) = 0

各部分を別個に解く

tan (θ) = 0 or sec (θ) + 2 = 0 or sec (θ) - 2 = 0

tan (θ) = 0, 0 \leq θ \leq 36 0^{\circ} : θ = 0, θ = 18 0^{\circ}, θ = 36 0^{\circ}

tan (θ) = 0, 0 \leq θ \leq 36 0^{\circ}

以下の一般解

tan (θ) = 0

tan (x)

18 0^{\circ} n

循環を含む周期性テーブル:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

θ = 0 + 18 0^{\circ} n

θ = 0 + 18 0^{\circ} n

解く

θ = 0 + 18 0^{\circ} n : θ = 18 0^{\circ} n

θ = 0 + 18 0^{\circ} n

0 + 18 0^{\circ} n = 18 0^{\circ} n

θ = 18 0^{\circ} n

θ = 18 0^{\circ} n

範囲の解答

0 \leq θ \leq 36 0^{\circ}

θ = 0, θ = 18 0^{\circ}, θ = 36 0^{\circ}

sec (θ) + 2 = 0, 0 \leq θ \leq 36 0^{\circ} : θ = 13 5^{\circ}, θ = 22 5^{\circ}

sec (θ) + 2 = 0, 0 \leq θ \leq 36 0^{\circ}

2

を右側に移動します

sec (θ) + 2 = 0

両辺から

2

を引く

sec (θ) + 2 - 2 = 0 - 2

簡素化

sec (θ) = - 2

sec (θ) = - 2

以下の一般解

sec (θ) = - 2

sec (x)

36 0^{\circ} n

循環を含む周期性テーブル :

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

θ = 13 5^{\circ} + 36 0^{\circ} n, θ = 22 5^{\circ} + 36 0^{\circ} n

θ = 13 5^{\circ} + 36 0^{\circ} n, θ = 22 5^{\circ} + 36 0^{\circ} n

範囲の解答

0 \leq θ \leq 36 0^{\circ}

θ = 13 5^{\circ}, θ = 22 5^{\circ}

sec (θ) - 2 = 0, 0 \leq θ \leq 36 0^{\circ} : θ = 4 5^{\circ}, θ = 31 5^{\circ}

sec (θ) - 2 = 0, 0 \leq θ \leq 36 0^{\circ}

2

を右側に移動します

sec (θ) - 2 = 0

両辺に

2

を足す

sec (θ) - 2 + 2 = 0 + 2

簡素化

sec (θ) = 2

sec (θ) = 2

以下の一般解

sec (θ) = 2

sec (x)

36 0^{\circ} n

循環を含む周期性テーブル :

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

θ = 4 5^{\circ} + 36 0^{\circ} n, θ = 31 5^{\circ} + 36 0^{\circ} n

θ = 4 5^{\circ} + 36 0^{\circ} n, θ = 31 5^{\circ} + 36 0^{\circ} n

範囲の解答

0 \leq θ \leq 36 0^{\circ}

θ = 4 5^{\circ}, θ = 31 5^{\circ}

すべての解を組み合わせる

θ = 0, θ = 18 0^{\circ}, θ = 36 0^{\circ}, θ = 13 5^{\circ}, θ = 22 5^{\circ}, θ = 4 5^{\circ}, θ = 31 5^{\circ}

グラフ

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