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受欢迎的三角函数 >

cos(2arccos(3/4))

解答

cos (2 arccos (\frac{3}{4}))

解答

\frac{1}{8}

+1

十进制

0.125

求解步骤

cos (2 arccos (\frac{3}{4}))

使用三角恒等式改写:

2 cos^{2} (arccos (\frac{3}{4})) - 1

cos (2 arccos (\frac{3}{4}))

使用倍角公式:

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

= 2 cos^{2} (arccos (\frac{3}{4})) - 1

= 2 cos^{2} (arccos (\frac{3}{4})) - 1

使用三角恒等式改写:

cos (arccos (\frac{3}{4})) = \frac{3}{4}

利用以下特性:

cos (arccos (x)) = x

= \frac{3}{4}

= 2 (\frac{3}{4})^{2} - 1

化简

2 (\frac{3}{4})^{2} - 1 : \frac{1}{8}

2 (\frac{3}{4})^{2} - 1

2 (\frac{3}{4})^{2} = \frac{9}{8}

2 (\frac{3}{4})^{2}

(\frac{3}{4})^{2} = \frac{3 ^{2}}{4 ^{2}}

(\frac{3}{4})^{2}

使用指数法则:

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

= \frac{3 ^{2}}{4 ^{2}}

= 2 \cdot \frac{3 ^{2}}{4 ^{2}}

分式相乘:

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

= \frac{3 ^{2} \cdot 2}{4 ^{2}}

分解

4^{2} : 2^{4}

因式分解

4 = 2^{2}

= (2^{2})^{2}

化简

(2^{2})^{2} : 2^{4}

(2^{2})^{2}

使用指数法则:

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

= 2^{2 \cdot 2}

数字相乘:

2 \cdot 2 = 4

= 2^{4}

= 2^{4}

= \frac{3 ^{2} \cdot 2}{2 ^{4}}

约分:

2

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

3^{2} = 9

= \frac{9}{2 ^{3}}

2^{3} = 8

= \frac{9}{8}

= \frac{9}{8} - 1

将项转换为分式:

1 = \frac{1 \cdot 8}{8}

= - \frac{1 \cdot 8}{8} + \frac{9}{8}

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 8 + 9}{8}

- 1 \cdot 8 + 9 = 1

- 1 \cdot 8 + 9

数字相乘:

1 \cdot 8 = 8

= - 8 + 9

数字相加/相减:

- 8 + 9 = 1

= 1

= \frac{1}{8}

= \frac{1}{8}

流行的例子

arcsec (2.5)

cot(arccos((-3)/4))

cot (arccos (\frac{- 3}{4}))

sin (168 0^{\circ})

arcsin (0.545)

1 - cos (\frac{2 π}{3})