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受欢迎的三角函数 >

3=20.39sin(θ)cos(θ)

解答

3 = 20.39 sin (θ) cos (θ)

解答

θ = \frac{0.29868 \dots}{2} + πn, θ = \frac{π}{2} - \frac{0.29868 \dots}{2} + πn

+1

度数

θ = 8.55664 \dots^{\circ} + 18 0^{\circ} n, θ = 81.44335 \dots^{\circ} + 18 0^{\circ} n

求解步骤

3 = 20.39 sin (θ) cos (θ)

交换两边

20.39 sin (θ) cos (θ) = 3

使用三角恒等式改写

20.39 sin (θ) cos (θ)

使用倍角公式:

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

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

= 20.39 \cdot \frac{sin ( 2 θ )}{2}

20.39 \cdot \frac{sin ( 2 θ )}{2} = 3

整理

20.39 \cdot \frac{sin ( 2 θ )}{2} : \frac{20.39 sin ( 2 θ )}{2}

20.39 \cdot \frac{sin ( 2 θ )}{2}

分式相乘:

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

= \frac{sin ( 2 θ ) \cdot 20.39}{2}

\frac{20.39 sin ( 2 θ )}{2} = 3

在两边乘以

2

\frac{20.39 sin ( 2 θ )}{2} = 3

在两边乘以

2

\frac{20.39 sin ( 2 θ )}{2} \cdot 2 = 3 \cdot 2

化简

\frac{20.39 sin ( 2 θ )}{2} \cdot 2 = 3 \cdot 2

化简

\frac{20.39 sin ( 2 θ )}{2} \cdot 2 : 20.39 sin (2 θ)

\frac{20.39 sin ( 2 θ )}{2} \cdot 2

分式相乘:

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

= \frac{20.39 sin ( 2 θ ) \cdot 2}{2}

约分:

2

= 20.39 sin (2 θ)

化简

3 \cdot 2 : 6

3 \cdot 2

数字相乘:

3 \cdot 2 = 6

= 6

20.39 sin (2 θ) = 6

20.39 sin (2 θ) = 6

20.39 sin (2 θ) = 6

两边除以

20.39

20.39 sin (2 θ) = 6

两边除以

20.39

\frac{20.39 sin ( 2 θ )}{20.39} = \frac{6}{20.39}

化简

sin (2 θ) = 0.29426 \dots

sin (2 θ) = 0.29426 \dots

使用反三角函数性质

sin (2 θ) = 0.29426 \dots

sin (2 θ) = 0.29426 \dots

的通解

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

2 θ = arcsin (0.29426 \dots) + 2 πn, 2 θ = π - arcsin (0.29426 \dots) + 2 πn

2 θ = arcsin (0.29426 \dots) + 2 πn, 2 θ = π - arcsin (0.29426 \dots) + 2 πn

解

2 θ = arcsin (0.29426 \dots) + 2 πn : θ = \frac{arcsin ( 0.29426 \dots )}{2} + πn

2 θ = arcsin (0.29426 \dots) + 2 πn

两边除以

2

2 θ = arcsin (0.29426 \dots) + 2 πn

两边除以

2

\frac{2 θ}{2} = \frac{arcsin ( 0.29426 \dots )}{2} + \frac{2 πn}{2}

化简

θ = \frac{arcsin ( 0.29426 \dots )}{2} + πn

θ = \frac{arcsin ( 0.29426 \dots )}{2} + πn

解

2 θ = π - arcsin (0.29426 \dots) + 2 πn : θ = \frac{π}{2} - \frac{arcsin ( 0.29426 \dots )}{2} + πn

2 θ = π - arcsin (0.29426 \dots) + 2 πn

两边除以

2

2 θ = π - arcsin (0.29426 \dots) + 2 πn

两边除以

2

\frac{2 θ}{2} = \frac{π}{2} - \frac{arcsin ( 0.29426 \dots )}{2} + \frac{2 πn}{2}

化简

θ = \frac{π}{2} - \frac{arcsin ( 0.29426 \dots )}{2} + πn

θ = \frac{π}{2} - \frac{arcsin ( 0.29426 \dots )}{2} + πn

θ = \frac{arcsin ( 0.29426 \dots )}{2} + πn, θ = \frac{π}{2} - \frac{arcsin ( 0.29426 \dots )}{2} + πn

以小数形式表示解

θ = \frac{0.29868 \dots}{2} + πn, θ = \frac{π}{2} - \frac{0.29868 \dots}{2} + πn

作图

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