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受欢迎的三角函数 >

885cos(θ)-70=cos(250)+250

解答

885 cos (θ) - 70 = cos (25 0^{\circ}) + 25 0^{\circ}

解答

θ = 1.48705 \dots + 36 0^{\circ} n, θ = 36 0^{\circ} - 1.48705 \dots + 36 0^{\circ} n

+1

弧度

θ = 1.48705 \dots + 2 πn, θ = 2 π - 1.48705 \dots + 2 πn

求解步骤

885 cos (θ) - 70 = cos (25 0^{\circ}) + 25 0^{\circ}

将

70

到右边

885 cos (θ) - 70 = cos (25 0^{\circ}) + 25 0^{\circ}

两边加上

70

885 cos (θ) - 70 + 70 = cos (25 0^{\circ}) + 25 0^{\circ} + 70

化简

885 cos (θ) = cos (25 0^{\circ}) + 25 0^{\circ} + 70

885 cos (θ) = cos (25 0^{\circ}) + 25 0^{\circ} + 70

两边除以

885

885 cos (θ) = cos (25 0^{\circ}) + 25 0^{\circ} + 70

两边除以

885

\frac{885 cos ( θ )}{885} = \frac{cos ( 25 0 ^{\circ} )}{885} + \frac{25 0 ^{\circ}}{885} + \frac{70}{885}

化简

\frac{885 cos ( θ )}{885} = \frac{cos ( 25 0 ^{\circ} )}{885} + \frac{25 0 ^{\circ}}{885} + \frac{70}{885}

化简

\frac{885 cos ( θ )}{885} : cos (θ)

\frac{885 cos ( θ )}{885}

数字相除:

\frac{885}{885} = 1

= cos (θ)

化简

\frac{cos ( 25 0 ^{\circ} )}{885} + \frac{25 0 ^{\circ}}{885} + \frac{70}{885} : \frac{18 cos ( 25 0 ^{\circ} ) + 450 0 ^{\circ} + 1260}{15930}

\frac{cos ( 25 0 ^{\circ} )}{885} + \frac{25 0 ^{\circ}}{885} + \frac{70}{885}

使用法则

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

= \frac{cos ( 25 0 ^{\circ} ) + 25 0 ^{\circ} + 70}{885}

化简

cos (25 0^{\circ}) + 25 0^{\circ} + 70 : \frac{18 cos ( 25 0 ^{\circ} ) + 450 0 ^{\circ} + 1260}{18}

cos (25 0^{\circ}) + 25 0^{\circ} + 70

将项转换为分式:

cos (25 0^{\circ}) = \frac{cos ( 25 0 ^{\circ} ) 18}{18}, 70 = \frac{70 \cdot 18}{18}

= \frac{cos ( 25 0 ^{\circ} ) \cdot 18}{18} + 25 0^{\circ} + \frac{70 \cdot 18}{18}

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{cos ( 25 0 ^{\circ} ) \cdot 18 + 450 0 ^{\circ} + 70 \cdot 18}{18}

数字相乘:

70 \cdot 18 = 1260

= \frac{18 cos ( 25 0 ^{\circ} ) + 450 0 ^{\circ} + 1260}{18}

= \frac{\frac{18 c o s ( 25 0 ^{\circ} ) + 450 0 ^{\circ} + 1260}{18}}{885}

使用分式法则:

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

= \frac{cos ( 25 0 ^{\circ} ) \cdot 18 + 450 0 ^{\circ} + 1260}{18 \cdot 885}

数字相乘:

18 \cdot 885 = 15930

= \frac{18 cos ( 25 0 ^{\circ} ) + 450 0 ^{\circ} + 1260}{15930}

cos (θ) = \frac{18 cos ( 25 0 ^{\circ} ) + 450 0 ^{\circ} + 1260}{15930}

cos (θ) = \frac{18 cos ( 25 0 ^{\circ} ) + 450 0 ^{\circ} + 1260}{15930}

cos (θ) = \frac{18 cos ( 25 0 ^{\circ} ) + 450 0 ^{\circ} + 1260}{15930}

使用反三角函数性质

cos (θ) = \frac{18 cos ( 25 0 ^{\circ} ) + 450 0 ^{\circ} + 1260}{15930}

cos (θ) = \frac{18 cos ( 25 0 ^{\circ} ) + 450 0 ^{\circ} + 1260}{15930}

的通解

cos (x) = a \Rightarrow x = arccos (a) + 36 0^{\circ} n, x = 36 0^{\circ} - arccos (a) + 36 0^{\circ} n

θ = arccos (\frac{18 cos ( 25 0 ^{\circ} ) + 450 0 ^{\circ} + 1260}{15930}) + 36 0^{\circ} n, θ = 36 0^{\circ} - arccos (\frac{18 cos ( 25 0 ^{\circ} ) + 450 0 ^{\circ} + 1260}{15930}) + 36 0^{\circ} n

θ = arccos (\frac{18 cos ( 25 0 ^{\circ} ) + 450 0 ^{\circ} + 1260}{15930}) + 36 0^{\circ} n, θ = 36 0^{\circ} - arccos (\frac{18 cos ( 25 0 ^{\circ} ) + 450 0 ^{\circ} + 1260}{15930}) + 36 0^{\circ} n

以小数形式表示解

θ = 1.48705 \dots + 36 0^{\circ} n, θ = 36 0^{\circ} - 1.48705 \dots + 36 0^{\circ} n

作图

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