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人気のある三角関数 >

(sin(115))/(20)=(sin(b))/(11)

解

\frac{sin ( 11 5 ^{\circ} )}{20} = \frac{sin ( b )}{11}

解

b = 0.52183 \dots + 36 0^{\circ} n, b = 18 0^{\circ} - 0.52183 \dots + 36 0^{\circ} n

+1

ラジアン

b = 0.52183 \dots + 2 πn, b = π - 0.52183 \dots + 2 πn

解答ステップ

\frac{sin ( 11 5 ^{\circ} )}{20} = \frac{sin ( b )}{11}

辺を交換する

\frac{sin ( b )}{11} = \frac{sin ( 11 5 ^{\circ} )}{20}

以下で両辺を乗じる:

10

\frac{sin ( b )}{11} = \frac{sin ( 11 5 ^{\circ} )}{20}

以下で両辺を乗じる:

10

\frac{sin ( b )}{11} \cdot 10 = \frac{sin ( 11 5 ^{\circ} )}{20} \cdot 10

簡素化

\frac{sin ( b )}{11} \cdot 10 = \frac{sin ( 11 5 ^{\circ} )}{20} \cdot 10

簡素化

\frac{sin ( b )}{11} \cdot 10 : \frac{10 sin ( b )}{11}

\frac{sin ( b )}{11} \cdot 10

分数を乗じる:

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

= \frac{sin ( b ) \cdot 10}{11}

簡素化

\frac{sin ( 11 5 ^{\circ} )}{20} \cdot 10 : \frac{sin ( 11 5 ^{\circ} )}{2}

\frac{sin ( 11 5 ^{\circ} )}{20} \cdot 10

分数を乗じる:

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

= \frac{sin ( 11 5 ^{\circ} ) \cdot 10}{20}

共通因数を約分する:

10

= \frac{sin ( 11 5 ^{\circ} )}{2}

\frac{10 sin ( b )}{11} = \frac{sin ( 11 5 ^{\circ} )}{2}

\frac{10 sin ( b )}{11} = \frac{sin ( 11 5 ^{\circ} )}{2}

\frac{10 sin ( b )}{11} = \frac{sin ( 11 5 ^{\circ} )}{2}

以下で両辺を乗じる:

11

\frac{10 sin ( b )}{11} = \frac{sin ( 11 5 ^{\circ} )}{2}

以下で両辺を乗じる:

11

\frac{11 \cdot 10 sin ( b )}{11} = \frac{11 sin ( 11 5 ^{\circ} )}{2}

簡素化

10 sin (b) = \frac{11 sin ( 11 5 ^{\circ} )}{2}

10 sin (b) = \frac{11 sin ( 11 5 ^{\circ} )}{2}

以下で両辺を割る

10

10 sin (b) = \frac{11 sin ( 11 5 ^{\circ} )}{2}

以下で両辺を割る

10

\frac{10 sin ( b )}{10} = \frac{\frac{11 s i n ( 11 5 ^{\circ} )}{2}}{10}

簡素化

\frac{10 sin ( b )}{10} = \frac{\frac{11 s i n ( 11 5 ^{\circ} )}{2}}{10}

簡素化

\frac{10 sin ( b )}{10} : sin (b)

\frac{10 sin ( b )}{10}

数を割る:

\frac{10}{10} = 1

= sin (b)

簡素化

\frac{\frac{11 s i n ( 11 5 ^{\circ} )}{2}}{10} : \frac{11 sin ( 11 5 ^{\circ} )}{20}

\frac{\frac{11 s i n ( 11 5 ^{\circ} )}{2}}{10}

分数の規則を適用する:

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

= \frac{11 sin ( 11 5 ^{\circ} )}{2 \cdot 10}

数を乗じる:

2 \cdot 10 = 20

= \frac{11 sin ( 11 5 ^{\circ} )}{20}

sin (b) = \frac{11 sin ( 11 5 ^{\circ} )}{20}

sin (b) = \frac{11 sin ( 11 5 ^{\circ} )}{20}

sin (b) = \frac{11 sin ( 11 5 ^{\circ} )}{20}

三角関数の逆数プロパティを適用する

sin (b) = \frac{11 sin ( 11 5 ^{\circ} )}{20}

以下の一般解

sin (b) = \frac{11 sin ( 11 5 ^{\circ} )}{20}

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

b = arcsin (\frac{11 sin ( 11 5 ^{\circ} )}{20}) + 36 0^{\circ} n, b = 18 0^{\circ} - arcsin (\frac{11 sin ( 11 5 ^{\circ} )}{20}) + 36 0^{\circ} n

b = arcsin (\frac{11 sin ( 11 5 ^{\circ} )}{20}) + 36 0^{\circ} n, b = 18 0^{\circ} - arcsin (\frac{11 sin ( 11 5 ^{\circ} )}{20}) + 36 0^{\circ} n

10進法形式で解を証明する

b = 0.52183 \dots + 36 0^{\circ} n, b = 18 0^{\circ} - 0.52183 \dots + 36 0^{\circ} n

グラフ

人気の例

cos(θ)=(25)/(sqrt(714))

cos (θ) = \frac{25}{714}

3sec^2(x)-4=0,0<= x<2pi

3 sec^{2} (x) - 4 = 0, 0 \leq x < 2 π

3cos(2x)+7sin(x)-5=0

3 cos (2 x) + 7 sin (x) - 5 = 0

cos^{2} (θ) = \frac{1}{3}

solvefor x,sin(x/5)=-(sqrt(3))/2

so l v e f or x, sin (\frac{x}{5}) = - \frac{3}{2}