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受欢迎的三角函数 >

sin(θ)=(0.3924)/(cos(θ))

解答

sin (θ) = \frac{0.3924}{cos ( θ )}

解答

θ = \frac{0.90237 \dots}{2} + πn, θ = \frac{π}{2} - \frac{0.90237 \dots}{2} + πn

+1

度数

θ = 25.85109 \dots^{\circ} + 18 0^{\circ} n, θ = 64.14890 \dots^{\circ} + 18 0^{\circ} n

求解步骤

sin (θ) = \frac{0.3924}{cos ( θ )}

两边减去

\frac{0.3924}{cos ( θ )}

sin (θ) - \frac{0.3924}{cos ( θ )} = 0

化简

sin (θ) - \frac{0.3924}{cos ( θ )} : \frac{sin ( θ ) cos ( θ ) - 0.3924}{cos ( θ )}

sin (θ) - \frac{0.3924}{cos ( θ )}

将项转换为分式:

sin (θ) = \frac{sin ( θ ) cos ( θ )}{cos ( θ )}

= \frac{sin ( θ ) cos ( θ )}{cos ( θ )} - \frac{0.3924}{cos ( θ )}

因为分母相等，所以合并分式:

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

= \frac{sin ( θ ) cos ( θ ) - 0.3924}{cos ( θ )}

\frac{sin ( θ ) cos ( θ ) - 0.3924}{cos ( θ )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

sin (θ) cos (θ) - 0.3924 = 0

使用三角恒等式改写

sin (θ) cos (θ) - 0.3924

使用倍角公式:

2 sin (x) cos (x) = sin (2 x)

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

= - 0.3924 + \frac{sin ( 2 θ )}{2}

- 0.3924 + \frac{sin ( 2 θ )}{2} = 0

将

0.3924

到右边

- 0.3924 + \frac{sin ( 2 θ )}{2} = 0

两边加上

0.3924

- 0.3924 + \frac{sin ( 2 θ )}{2} + 0.3924 = 0 + 0.3924

化简

\frac{sin ( 2 θ )}{2} = 0.3924

\frac{sin ( 2 θ )}{2} = 0.3924

在两边乘以

2

\frac{sin ( 2 θ )}{2} = 0.3924

在两边乘以

2

\frac{2 sin ( 2 θ )}{2} = 0.3924 \cdot 2

化简

sin (2 θ) = 0.7848

sin (2 θ) = 0.7848

使用反三角函数性质

sin (2 θ) = 0.7848

sin (2 θ) = 0.7848

的通解

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

2 θ = arcsin (0.7848) + 2 πn, 2 θ = π - arcsin (0.7848) + 2 πn

2 θ = arcsin (0.7848) + 2 πn, 2 θ = π - arcsin (0.7848) + 2 πn

解

2 θ = arcsin (0.7848) + 2 πn : θ = \frac{arcsin ( 0.7848 )}{2} + πn

2 θ = arcsin (0.7848) + 2 πn

两边除以

2

2 θ = arcsin (0.7848) + 2 πn

两边除以

2

\frac{2 θ}{2} = \frac{arcsin ( 0.7848 )}{2} + \frac{2 πn}{2}

化简

θ = \frac{arcsin ( 0.7848 )}{2} + πn

θ = \frac{arcsin ( 0.7848 )}{2} + πn

解

2 θ = π - arcsin (0.7848) + 2 πn : θ = \frac{π}{2} - \frac{arcsin ( 0.7848 )}{2} + πn

2 θ = π - arcsin (0.7848) + 2 πn

两边除以

2

2 θ = π - arcsin (0.7848) + 2 πn

两边除以

2

\frac{2 θ}{2} = \frac{π}{2} - \frac{arcsin ( 0.7848 )}{2} + \frac{2 πn}{2}

化简

θ = \frac{π}{2} - \frac{arcsin ( 0.7848 )}{2} + πn

θ = \frac{π}{2} - \frac{arcsin ( 0.7848 )}{2} + πn

θ = \frac{arcsin ( 0.7848 )}{2} + πn, θ = \frac{π}{2} - \frac{arcsin ( 0.7848 )}{2} + πn

以小数形式表示解

θ = \frac{0.90237 \dots}{2} + πn, θ = \frac{π}{2} - \frac{0.90237 \dots}{2} + πn

作图

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