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受欢迎的三角函数 >

1/2 (6.50941)+cos(θ)(10.40478)=12

解答

\frac{1}{2} (6.50941) + cos (θ) (10.40478) = 12

解答

θ = 0.57257 \dots + 2 πn, θ = 2 π - 0.57257 \dots + 2 πn

+1

度数

θ = 32.80625 \dots^{\circ} + 36 0^{\circ} n, θ = 327.19374 \dots^{\circ} + 36 0^{\circ} n

求解步骤

\frac{1}{2} (6.50941) + cos (θ) (10.40478) = 12

\frac{1}{2} \cdot 6.50941 = \frac{6.50941}{2}

\frac{1}{2} \cdot 6.50941

分式相乘:

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

= \frac{1 \cdot 6.50941}{2}

数字相乘:

1 \cdot 6.50941 = 6.50941

= \frac{6.50941}{2}

\frac{6.50941}{2} + 10.40478 cos (θ) = 12

将

\frac{6.50941}{2}

到右边

\frac{6.50941}{2} + 10.40478 cos (θ) = 12

两边减去

\frac{6.50941}{2}

\frac{6.50941}{2} + 10.40478 cos (θ) - \frac{6.50941}{2} = 12 - \frac{6.50941}{2}

化简

\frac{6.50941}{2} + 10.40478 cos (θ) - \frac{6.50941}{2} = 12 - \frac{6.50941}{2}

化简

\frac{6.50941}{2} + 10.40478 cos (θ) - \frac{6.50941}{2} : 10.40478 cos (θ)

\frac{6.50941}{2} + 10.40478 cos (θ) - \frac{6.50941}{2}

同类项相加:

\frac{6.50941}{2} - \frac{6.50941}{2} = 0

= 10.40478 cos (θ)

化简

12 - \frac{6.50941}{2} : \frac{17.49059}{2}

12 - \frac{6.50941}{2}

将项转换为分式:

12 = \frac{12 \cdot 2}{2}

= \frac{12 \cdot 2}{2} - \frac{6.50941}{2}

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{12 \cdot 2 - 6.50941}{2}

12 \cdot 2 - 6.50941 = 17.49059

12 \cdot 2 - 6.50941

数字相乘:

12 \cdot 2 = 24

= 24 - 6.50941

数字相减:

24 - 6.50941 = 17.49059

= 17.49059

= \frac{17.49059}{2}

10.40478 cos (θ) = \frac{17.49059}{2}

10.40478 cos (θ) = \frac{17.49059}{2}

10.40478 cos (θ) = \frac{17.49059}{2}

两边除以

10.40478

10.40478 cos (θ) = \frac{17.49059}{2}

两边除以

10.40478

\frac{10.40478 cos ( θ )}{10.40478} = \frac{\frac{17.49059}{2}}{10.40478}

化简

\frac{10.40478 cos ( θ )}{10.40478} = \frac{\frac{17.49059}{2}}{10.40478}

化简

\frac{10.40478 cos ( θ )}{10.40478} : cos (θ)

\frac{10.40478 cos ( θ )}{10.40478}

约分:

10.40478

= cos (θ)

化简

\frac{\frac{17.49059}{2}}{10.40478} : \frac{17.49059}{20.80956}

\frac{\frac{17.49059}{2}}{10.40478}

使用分式法则:

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

= \frac{17.49059}{2 \cdot 10.40478}

数字相乘:

2 \cdot 10.40478 = 20.80956

= \frac{17.49059}{20.80956}

cos (θ) = \frac{17.49059}{20.80956}

cos (θ) = \frac{17.49059}{20.80956}

cos (θ) = \frac{17.49059}{20.80956}

使用反三角函数性质

cos (θ) = \frac{17.49059}{20.80956}

cos (θ) = \frac{17.49059}{20.80956}

的通解

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

θ = arccos (\frac{17.49059}{20.80956}) + 2 πn, θ = 2 π - arccos (\frac{17.49059}{20.80956}) + 2 πn

θ = arccos (\frac{17.49059}{20.80956}) + 2 πn, θ = 2 π - arccos (\frac{17.49059}{20.80956}) + 2 πn

以小数形式表示解

θ = 0.57257 \dots + 2 πn, θ = 2 π - 0.57257 \dots + 2 πn

作图

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