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受欢迎的三角函数 >

(sin(115))/(20)=(sin(B))/(15)

解答

\frac{sin ( 11 5 ^{\circ} )}{20} = \frac{sin ( B )}{15}

解答

B = 0.74739 \dots + 36 0^{\circ} n, B = 18 0^{\circ} - 0.74739 \dots + 36 0^{\circ} n

+1

弧度

B = 0.74739 \dots + 2 πn, B = π - 0.74739 \dots + 2 πn

求解步骤

\frac{sin ( 11 5 ^{\circ} )}{20} = \frac{sin ( B )}{15}

交换两边

\frac{sin ( B )}{15} = \frac{sin ( 11 5 ^{\circ} )}{20}

在两边乘以

10

\frac{sin ( B )}{15} = \frac{sin ( 11 5 ^{\circ} )}{20}

在两边乘以

10

\frac{sin ( B )}{15} \cdot 10 = \frac{sin ( 11 5 ^{\circ} )}{20} \cdot 10

化简

\frac{sin ( B )}{15} \cdot 10 = \frac{sin ( 11 5 ^{\circ} )}{20} \cdot 10

化简

\frac{sin ( B )}{15} \cdot 10 : \frac{2 sin ( B )}{3}

\frac{sin ( B )}{15} \cdot 10

分式相乘:

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

= \frac{sin ( B ) \cdot 10}{15}

约分:

5

= \frac{2 sin ( B )}{3}

化简

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

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

分式相乘:

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

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

约分:

10

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

\frac{2 sin ( B )}{3} = \frac{sin ( 11 5 ^{\circ} )}{2}

\frac{2 sin ( B )}{3} = \frac{sin ( 11 5 ^{\circ} )}{2}

\frac{2 sin ( B )}{3} = \frac{sin ( 11 5 ^{\circ} )}{2}

在两边乘以

3

\frac{2 sin ( B )}{3} = \frac{sin ( 11 5 ^{\circ} )}{2}

在两边乘以

3

\frac{3 \cdot 2 sin ( B )}{3} = \frac{3 sin ( 11 5 ^{\circ} )}{2}

化简

2 sin (B) = \frac{3 sin ( 11 5 ^{\circ} )}{2}

2 sin (B) = \frac{3 sin ( 11 5 ^{\circ} )}{2}

两边除以

2

2 sin (B) = \frac{3 sin ( 11 5 ^{\circ} )}{2}

两边除以

2

\frac{2 sin ( B )}{2} = \frac{\frac{3 s i n ( 11 5 ^{\circ} )}{2}}{2}

化简

\frac{2 sin ( B )}{2} = \frac{\frac{3 s i n ( 11 5 ^{\circ} )}{2}}{2}

化简

\frac{2 sin ( B )}{2} : sin (B)

\frac{2 sin ( B )}{2}

数字相除:

\frac{2}{2} = 1

= sin (B)

化简

\frac{\frac{3 s i n ( 11 5 ^{\circ} )}{2}}{2} : \frac{3 sin ( 11 5 ^{\circ} )}{4}

\frac{\frac{3 s i n ( 11 5 ^{\circ} )}{2}}{2}

使用分式法则:

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

= \frac{3 sin ( 11 5 ^{\circ} )}{2 \cdot 2}

数字相乘:

2 \cdot 2 = 4

= \frac{3 sin ( 11 5 ^{\circ} )}{4}

sin (B) = \frac{3 sin ( 11 5 ^{\circ} )}{4}

sin (B) = \frac{3 sin ( 11 5 ^{\circ} )}{4}

sin (B) = \frac{3 sin ( 11 5 ^{\circ} )}{4}

使用反三角函数性质

sin (B) = \frac{3 sin ( 11 5 ^{\circ} )}{4}

sin (B) = \frac{3 sin ( 11 5 ^{\circ} )}{4}

的通解

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

B = arcsin (\frac{3 sin ( 11 5 ^{\circ} )}{4}) + 36 0^{\circ} n, B = 18 0^{\circ} - arcsin (\frac{3 sin ( 11 5 ^{\circ} )}{4}) + 36 0^{\circ} n

B = arcsin (\frac{3 sin ( 11 5 ^{\circ} )}{4}) + 36 0^{\circ} n, B = 18 0^{\circ} - arcsin (\frac{3 sin ( 11 5 ^{\circ} )}{4}) + 36 0^{\circ} n

以小数形式表示解

B = 0.74739 \dots + 36 0^{\circ} n, B = 18 0^{\circ} - 0.74739 \dots + 36 0^{\circ} n

作图

流行的例子

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sin (x) = - \frac{2}{2}, - π \leq x \leq π

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