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受欢迎的三角函数 >

1.5=(sin(45))/(sin(x))

解答

1.5 = \frac{sin ( 4 5 ^{\circ} )}{sin ( x )}

解答

x = 0.49088 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.49088 \dots + 36 0^{\circ} n

+1

弧度

x = 0.49088 \dots + 2 πn, x = π - 0.49088 \dots + 2 πn

求解步骤

1.5 = \frac{sin ( 4 5 ^{\circ} )}{sin ( x )}

交换两边

\frac{sin ( 4 5 ^{\circ} )}{sin ( x )} = 1.5

sin (4 5^{\circ}) = \frac{2}{2}

sin (4 5^{\circ})

使用以下普通恒等式:

sin (4 5^{\circ}) = \frac{2}{2}

sin (4 5^{\circ})

sin (x)

周期表（周期为

36 0^{\circ} n

"）：

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{2}{2}

= \frac{2}{2}

\frac{\frac{2}{2}}{sin ( x )} = 1.5

化简

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

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

使用分式法则:

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

= \frac{2}{2 sin ( x )}

\frac{2}{2 sin ( x )} = 1.5

在两边乘以

sin (x)

\frac{2}{2 sin ( x )} = 1.5

在两边乘以

sin (x)

\frac{2}{2 sin ( x )} sin (x) = 1.5 sin (x)

化简

\frac{2}{2} = 1.5 sin (x)

\frac{2}{2} = 1.5 sin (x)

交换两边

1.5 sin (x) = \frac{2}{2}

在两边乘以

10

1.5 sin (x) = \frac{2}{2}

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere is one digit to the right of the decimal point, therefore multiply by

10

1.5 sin (x) \cdot 10 = \frac{2}{2} \cdot 10

整理后得

15 sin (x) = 52

15 sin (x) = 52

两边除以

15

15 sin (x) = 52

两边除以

15

\frac{15 sin ( x )}{15} = \frac{5 2}{15}

化简

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

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

验证解

找到无定义的点（奇点）:

sin (x) = 0

取

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

的分母，令其等于零

sin (x) = 0

以下点无定义

sin (x) = 0

将不在定义域的点与解相综合:

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

使用反三角函数性质

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

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

的通解

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

x = arcsin (\frac{2}{3}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{2}{3}) + 36 0^{\circ} n

x = arcsin (\frac{2}{3}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{2}{3}) + 36 0^{\circ} n

以小数形式表示解

x = 0.49088 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.49088 \dots + 36 0^{\circ} n

作图

流行的例子

sin(4x)+sin(6x)=0

sin (4 x) + sin (6 x) = 0

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tan^2(θ)=2sec(θ)-1

tan^{2} (θ) = 2 sec (θ) - 1