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人気のある三角関数 >

tan^2(x)=sqrt(3)

解

tan^{2} (x) = 3

解

x = 0.92103 \dots + πn, x = - 0.92103 \dots + πn

+1

度

x = 52.77113 \dots^{\circ} + 18 0^{\circ} n, x = - 52.77113 \dots^{\circ} + 18 0^{\circ} n

解答ステップ

tan^{2} (x) = 3

置換で解く

tan^{2} (x) = 3

仮定:

tan (x) = u

u^{2} = 3

u^{2} = 3 : u = 43, u = - 43

u^{2} = 3

x^{2} = f (a)

の場合, 解は

x = f (a), - f (a)

u = 3, u = - 3

3 = 43

3

累乗根の規則を適用する:

a = a^{\frac{1}{2}}

= (3^{\frac{1}{2}})^{\frac{1}{2}}

指数の規則を適用する:

(a^{b})^{c} = a^{b c}

= 3^{\frac{1}{2} \cdot \frac{1}{2}}

\frac{1}{2} \cdot \frac{1}{2} = \frac{1}{4}

\frac{1}{2} \cdot \frac{1}{2}

分数を乗じる:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{1 \cdot 1}{2 \cdot 2}

数を乗じる:

1 \cdot 1 = 1

= \frac{1}{2 \cdot 2}

数を乗じる:

2 \cdot 2 = 4

= \frac{1}{4}

= 3^{\frac{1}{4}}

a^{\frac{1}{n}} = n a

= 43

- 3 = - 43

- 3

簡素化

3 : 43

3

累乗根の規則を適用する:

a = a^{\frac{1}{2}}

= (3^{\frac{1}{2}})^{\frac{1}{2}}

指数の規則を適用する:

(a^{b})^{c} = a^{b c}

= 3^{\frac{1}{2} \cdot \frac{1}{2}}

\frac{1}{2} \cdot \frac{1}{2} = \frac{1}{4}

\frac{1}{2} \cdot \frac{1}{2}

分数を乗じる:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{1 \cdot 1}{2 \cdot 2}

数を乗じる:

1 \cdot 1 = 1

= \frac{1}{2 \cdot 2}

数を乗じる:

2 \cdot 2 = 4

= \frac{1}{4}

= 3^{\frac{1}{4}}

a^{\frac{1}{n}} = n a

= 43

= - 43

u = 43, u = - 43

代用を戻す

u = tan (x)

tan (x) = 43, tan (x) = - 43

tan (x) = 43, tan (x) = - 43

tan (x) = 43 : x = arctan (43) + πn

tan (x) = 43

三角関数の逆数プロパティを適用する

tan (x) = 43

以下の一般解

tan (x) = 43

tan (x) = a \Rightarrow x = arctan (a) + πn

x = arctan (43) + πn

x = arctan (43) + πn

tan (x) = - 43 : x = arctan (- 43) + πn

tan (x) = - 43

三角関数の逆数プロパティを適用する

tan (x) = - 43

以下の一般解

tan (x) = - 43

tan (x) = - a \Rightarrow x = arctan (- a) + πn

x = arctan (- 43) + πn

x = arctan (- 43) + πn

すべての解を組み合わせる

x = arctan (43) + πn, x = arctan (- 43) + πn

10進法形式で解を証明する

x = 0.92103 \dots + πn, x = - 0.92103 \dots + πn

グラフ

人気の例

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