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受欢迎的三角函数 >

8cos(B)+sqrt(52)=0

解答

8 cos (B) + 52 = 0

解答

B = 2.69376 \dots + 2 πn, B = - 2.69376 \dots + 2 πn

+1

度数

B = 154.34109 \dots^{\circ} + 36 0^{\circ} n, B = - 154.34109 \dots^{\circ} + 36 0^{\circ} n

求解步骤

8 cos (B) + 52 = 0

52 = 213

52

52

质因数分解:

2^{2} \cdot 13

52

52

除以

252 = 26 \cdot 2

= 2 \cdot 26

26

除以

226 = 13 \cdot 2

= 2 \cdot 2 \cdot 13

2, 13

都是质数，因此无法进一步因数分解

= 2 \cdot 2 \cdot 13

= 2^{2} \cdot 13

= 2^{2} \cdot 13

使用根式运算法则:

n ab = n a n b

= 13 2^{2}

使用根式运算法则:

n a^{n} = a

2^{2} = 2

= 213

8 cos (B) + 213 = 0

将

213

到右边

8 cos (B) + 213 = 0

两边减去

213

8 cos (B) + 213 - 213 = 0 - 213

化简

8 cos (B) = - 213

8 cos (B) = - 213

两边除以

8

8 cos (B) = - 213

两边除以

8

\frac{8 cos ( B )}{8} = \frac{- 2 13}{8}

化简

\frac{8 cos ( B )}{8} = \frac{- 2 13}{8}

化简

\frac{8 cos ( B )}{8} : cos (B)

\frac{8 cos ( B )}{8}

数字相除:

\frac{8}{8} = 1

= cos (B)

化简

\frac{- 2 13}{8} : - \frac{13}{4}

\frac{- 2 13}{8}

使用分式法则:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{2 13}{8}

约分:

2

= - \frac{13}{4}

cos (B) = - \frac{13}{4}

cos (B) = - \frac{13}{4}

cos (B) = - \frac{13}{4}

使用反三角函数性质

cos (B) = - \frac{13}{4}

cos (B) = - \frac{13}{4}

的通解

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

B = arccos (- \frac{13}{4}) + 2 πn, B = - arccos (- \frac{13}{4}) + 2 πn

B = arccos (- \frac{13}{4}) + 2 πn, B = - arccos (- \frac{13}{4}) + 2 πn

以小数形式表示解

B = 2.69376 \dots + 2 πn, B = - 2.69376 \dots + 2 πn

作图

流行的例子

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

sin(5x)=(sqrt(3))/2

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sin^{2} (θ) - cos^{2} (θ) = - 1

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