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 >

cos(2arccos(1/3))

解答

cos (2 arccos (\frac{1}{3}))

解答

- \frac{7}{9}

+1

十进制

- 0.77777 \dots

求解步骤

cos (2 arccos (\frac{1}{3}))

使用三角恒等式改写:

2 cos^{2} (arccos (\frac{1}{3})) - 1

cos (2 arccos (\frac{1}{3}))

使用倍角公式:

cos (2 x) = 2 cos^{2} (x) - 1

= 2 cos^{2} (arccos (\frac{1}{3})) - 1

= 2 cos^{2} (arccos (\frac{1}{3})) - 1

使用三角恒等式改写:

cos (arccos (\frac{1}{3})) = \frac{1}{3}

利用以下特性:

cos (arccos (x)) = x

= \frac{1}{3}

= 2 (\frac{1}{3})^{2} - 1

化简

2 (\frac{1}{3})^{2} - 1 : - \frac{7}{9}

2 (\frac{1}{3})^{2} - 1

2 (\frac{1}{3})^{2} = \frac{2}{9}

2 (\frac{1}{3})^{2}

(\frac{1}{3})^{2} = \frac{1}{3 ^{2}}

(\frac{1}{3})^{2}

使用指数法则:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{1 ^{2}}{3 ^{2}}

使用法则

1^{a} = 1

1^{2} = 1

= \frac{1}{3 ^{2}}

= 2 \cdot \frac{1}{3 ^{2}}

分式相乘:

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

= \frac{1 \cdot 2}{3 ^{2}}

数字相乘:

1 \cdot 2 = 2

= \frac{2}{3 ^{2}}

3^{2} = 9

= \frac{2}{9}

= \frac{2}{9} - 1

将项转换为分式:

1 = \frac{1 \cdot 9}{9}

= - \frac{1 \cdot 9}{9} + \frac{2}{9}

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{- 1 \cdot 9 + 2}{9}

- 1 \cdot 9 + 2 = - 7

- 1 \cdot 9 + 2

数字相乘:

1 \cdot 9 = 9

= - 9 + 2

数字相加/相减:

- 9 + 2 = - 7

= - 7

= \frac{- 7}{9}

使用分式法则:

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

= - \frac{7}{9}

= - \frac{7}{9}

流行的例子

arcsin(cos((3pi)/5))

arcsin (cos (\frac{3 π}{5}))

arcsin((1.52*sin(51))/(1.33))

arcsin (\frac{1.52 \cdot sin ( 5 1 ^{\circ} )}{1.33})

\frac{20}{tan ( 1 5 ^{\circ} )}

cos(40)+cos(80)+cos(100)+cos(120)+cos(140)

cos (4 0^{\circ}) + cos (8 0^{\circ}) + cos (10 0^{\circ}) + cos (12 0^{\circ}) + cos (14 0^{\circ})

2sin(50)cos(50)

2 sin (5 0^{\circ}) cos (5 0^{\circ})