zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的三角函数 >

100=50sqrt(40)cos(θ)

解答

100 = 5040 cos (θ)

解答

θ = 1.24904 \dots + 2 πn, θ = 2 π - 1.24904 \dots + 2 πn

+1

度数

θ = 71.56505 \dots^{\circ} + 36 0^{\circ} n, θ = 288.43494 \dots^{\circ} + 36 0^{\circ} n

求解步骤

100 = 5040 cos (θ)

交换两边

5040 cos (θ) = 100

化简

5040 : 10010

5040

40 = 210

40

40

质因数分解:

2^{3} \cdot 5

40

40

除以

240 = 20 \cdot 2

= 2 \cdot 20

20

除以

220 = 10 \cdot 2

= 2 \cdot 2 \cdot 10

10

除以

210 = 5 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 5

2, 5

都是质数，因此无法进一步因数分解

= 2 \cdot 2 \cdot 2 \cdot 5

= 2^{3} \cdot 5

= 2^{3} \cdot 5

使用指数法则:

a^{b + c} = a^{b} \cdot a^{c}

= 2^{2} \cdot 2 \cdot 5

使用根式运算法则:

n ab = n a n b

= 2^{2} 2 \cdot 5

使用根式运算法则:

n a^{n} = a

2^{2} = 2

= 2 2 \cdot 5

整理后得

= 210

= 50 \cdot 210

数字相乘:

50 \cdot 2 = 100

= 10010

10010 cos (θ) = 100

两边除以

10010

10010 cos (θ) = 100

两边除以

10010

\frac{100 10 cos ( θ )}{100 10} = \frac{100}{100 10}

化简

\frac{100 10 cos ( θ )}{100 10} = \frac{100}{100 10}

化简

\frac{100 10 cos ( θ )}{100 10} : cos (θ)

\frac{100 10 cos ( θ )}{100 10}

数字相除:

\frac{100}{100} = 1

= \frac{10 cos ( θ )}{10}

约分:

10

= cos (θ)

化简

\frac{100}{100 10} : \frac{10}{10}

\frac{100}{100 10}

数字相除:

\frac{100}{100} = 1

= \frac{1}{10}

\frac{1}{10}

有理化:

\frac{10}{10}

\frac{1}{10}

乘以共轭根式

\frac{10}{10}

= \frac{1 \cdot 10}{10 10}

1 \cdot 10 = 10

1010 = 10

1010

使用根式运算法则:

a a = a

1010 = 10

= 10

= \frac{10}{10}

= \frac{10}{10}

cos (θ) = \frac{10}{10}

cos (θ) = \frac{10}{10}

cos (θ) = \frac{10}{10}

使用反三角函数性质

cos (θ) = \frac{10}{10}

cos (θ) = \frac{10}{10}

的通解

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

θ = arccos (\frac{10}{10}) + 2 πn, θ = 2 π - arccos (\frac{10}{10}) + 2 πn

θ = arccos (\frac{10}{10}) + 2 πn, θ = 2 π - arccos (\frac{10}{10}) + 2 πn

以小数形式表示解

θ = 1.24904 \dots + 2 πn, θ = 2 π - 1.24904 \dots + 2 πn

作图

流行的例子

cos (3 x) = \frac{2}{3}

4cos^3(x)-7cos(x)-3=0

4 cos^{3} (x) - 7 cos (x) - 3 = 0

(sin(θ))/(1.3)=(sin(125))/(2.8519)

\frac{sin ( θ )}{1.3} = \frac{sin ( 12 5 ^{\circ} )}{2.8519}

8sin(θ)cos(θ)tan(θ)=csc(θ)

8 sin (θ) cos (θ) tan (θ) = csc (θ)

(cot(θ))/(sec(θ))=sin(θ)

\frac{cot ( θ )}{sec ( θ )} = sin (θ)