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人気のある三角関数 >

8cos(x)+8sin(x)tan(x)=16

解

8 cos (x) + 8 sin (x) tan (x) = 16

解

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

+1

度

x = 6 0^{\circ} + 36 0^{\circ} n, x = 30 0^{\circ} + 36 0^{\circ} n

解答ステップ

8 cos (x) + 8 sin (x) tan (x) = 16

両辺から

16

を引く

8 cos (x) + 8 sin (x) tan (x) - 16 = 0

三角関数の公式を使用して書き換える

- 16 + 8 cos (x) + 8 sin (x) tan (x)

基本的な三角関数の公式を使用する:

tan (x) = \frac{sin ( x )}{cos ( x )}

= - 16 + 8 cos (x) + 8 sin (x) \frac{sin ( x )}{cos ( x )}

8 sin (x) \frac{sin ( x )}{cos ( x )} = \frac{8 sin ^{2} ( x )}{cos ( x )}

8 sin (x) \frac{sin ( x )}{cos ( x )}

分数を乗じる:

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

= \frac{sin ( x ) \cdot 8 sin ( x )}{cos ( x )}

sin (x) \cdot 8 sin (x) = 8 sin^{2} (x)

sin (x) \cdot 8 sin (x)

指数の規則を適用する:

a^{b} \cdot a^{c} = a^{b + c}

sin (x) sin (x) = sin^{1 + 1} (x)

= 8 sin^{1 + 1} (x)

数を足す:

1 + 1 = 2

= 8 sin^{2} (x)

= \frac{8 sin ^{2} ( x )}{cos ( x )}

= - 16 + 8 cos (x) + \frac{8 sin ^{2} ( x )}{cos ( x )}

ピタゴラスの公式を使用する:

cos^{2} (x) + sin^{2} (x) = 1

sin^{2} (x) = 1 - cos^{2} (x)

= - 16 + \frac{8 ( 1 - cos ^{2} ( x ) )}{cos ( x )} + 8 cos (x)

分数を組み合わせる

\frac{8 ( - cos ^{2} ( x ) + 1 )}{cos ( x )} + 8 cos (x) : \frac{8}{cos ( x )}

\frac{8 ( - cos ^{2} ( x ) + 1 )}{cos ( x )} + 8 cos (x)

元を分数に変換する:

8 cos (x) = \frac{8 cos ( x ) cos ( x )}{cos ( x )}

= \frac{8 ( 1 - cos ^{2} ( x ) )}{cos ( x )} + \frac{8 cos ( x ) cos ( x )}{cos ( x )}

分母が等しいので, 分数を組み合わせる:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{8 ( 1 - cos ^{2} ( x ) ) + 8 cos ( x ) cos ( x )}{cos ( x )}

8 (1 - cos^{2} (x)) + 8 cos (x) cos (x) = 8 (1 - cos^{2} (x)) + 8 cos^{2} (x)

8 (1 - cos^{2} (x)) + 8 cos (x) cos (x)

8 cos (x) cos (x) = 8 cos^{2} (x)

8 cos (x) cos (x)

指数の規則を適用する:

a^{b} \cdot a^{c} = a^{b + c}

cos (x) cos (x) = cos^{1 + 1} (x)

= 8 cos^{1 + 1} (x)

数を足す:

1 + 1 = 2

= 8 cos^{2} (x)

= 8 (- cos^{2} (x) + 1) + 8 cos^{2} (x)

= \frac{8 ( - cos ^{2} ( x ) + 1 ) + 8 cos ^{2} ( x )}{cos ( x )}

拡張

8 (1 - cos^{2} (x)) + 8 cos^{2} (x) : 8

8 (1 - cos^{2} (x)) + 8 cos^{2} (x)

拡張

8 (1 - cos^{2} (x)) : 8 - 8 cos^{2} (x)

8 (1 - cos^{2} (x))

分配法則を適用する:

a (b - c) = ab - a c

a = 8, b = 1, c = cos^{2} (x)

= 8 \cdot 1 - 8 cos^{2} (x)

数を乗じる:

8 \cdot 1 = 8

= 8 - 8 cos^{2} (x)

= 8 - 8 cos^{2} (x) + 8 cos^{2} (x)

類似した元を足す:

- 8 cos^{2} (x) + 8 cos^{2} (x) = 0

= 8

= \frac{8}{cos ( x )}

= \frac{8}{cos ( x )} - 16

- 16 + \frac{8}{cos ( x )} = 0

- 16 + \frac{8}{cos ( x )} = 0

以下で両辺を乗じる:

cos (x)

- 16 + \frac{8}{cos ( x )} = 0

以下で両辺を乗じる:

cos (x)

- 16 cos (x) + \frac{8}{cos ( x )} cos (x) = 0 \cdot cos (x)

簡素化

- 16 cos (x) + \frac{8}{cos ( x )} cos (x) = 0 \cdot cos (x)

簡素化

\frac{8}{cos ( x )} cos (x) : 8

\frac{8}{cos ( x )} cos (x)

分数を乗じる:

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

= \frac{8 cos ( x )}{cos ( x )}

共通因数を約分する:

cos (x)

= 8

簡素化

0 \cdot cos (x) : 0

0 \cdot cos (x)

規則を適用

0 \cdot a = 0

= 0

- 16 cos (x) + 8 = 0

- 16 cos (x) + 8 = 0

- 16 cos (x) + 8 = 0

8

を右側に移動します

- 16 cos (x) + 8 = 0

両辺から

8

を引く

- 16 cos (x) + 8 - 8 = 0 - 8

簡素化

- 16 cos (x) = - 8

- 16 cos (x) = - 8

以下で両辺を割る

- 16

- 16 cos (x) = - 8

以下で両辺を割る

- 16

\frac{- 16 cos ( x )}{- 16} = \frac{- 8}{- 16}

簡素化

\frac{- 16 cos ( x )}{- 16} = \frac{- 8}{- 16}

簡素化

\frac{- 16 cos ( x )}{- 16} : cos (x)

\frac{- 16 cos ( x )}{- 16}

分数の規則を適用する:

\frac{- a}{- b} = \frac{a}{b}

= \frac{16 cos ( x )}{16}

数を割る:

\frac{16}{16} = 1

= cos (x)

簡素化

\frac{- 8}{- 16} : \frac{1}{2}

\frac{- 8}{- 16}

分数の規則を適用する:

\frac{- a}{- b} = \frac{a}{b}

= \frac{8}{16}

共通因数を約分する:

8

= \frac{1}{2}

cos (x) = \frac{1}{2}

cos (x) = \frac{1}{2}

cos (x) = \frac{1}{2}

解を検算する

未定義の (特異) 点を求める:

cos (x) = 0

- 16 + \frac{8}{cos ( x )}

の分母をゼロに比較する

cos (x) = 0

以下の点は定義されていない

cos (x) = 0

未定義のポイントを解に組み合わせる:

cos (x) = \frac{1}{2}

以下の一般解

cos (x) = \frac{1}{2}

cos (x)

2 πn

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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} 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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

グラフ

人気の例

(sin(2x)-1)(2sin(2x)-1)=0

(sin (2 x) - 1) (2 sin (2 x) - 1) = 0

2cos^2(x)-cos(x)=2-sec(x)

2 cos^{2} (x) - cos (x) = 2 - sec (x)

sin^4(x)-cos^4(x)= 1/2

sin^{4} (x) - cos^{4} (x) = \frac{1}{2}

solvefor x,y=tan(x)

so l v e f or x, y = tan (x)

sin (θ) = - 2