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受欢迎的三角函数 >

cos(2arcsin(1/4))

解答

cos (2 arcsin (\frac{1}{4}))

解答

\frac{7}{8}

+1

十进制

0.875

求解步骤

cos (2 arcsin (\frac{1}{4}))

使用三角恒等式改写:

1 - 2 sin^{2} (arcsin (\frac{1}{4}))

cos (2 arcsin (\frac{1}{4}))

使用倍角公式:

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

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

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

使用三角恒等式改写:

sin (arcsin (\frac{1}{4})) = \frac{1}{4}

利用以下特性:

sin (arcsin (x)) = x

= \frac{1}{4}

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

化简

1 - 2 (\frac{1}{4})^{2} : \frac{7}{8}

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

2 (\frac{1}{4})^{2} = \frac{1}{8}

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

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

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

使用指数法则:

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

= \frac{1 ^{2}}{4 ^{2}}

使用法则

1^{a} = 1

1^{2} = 1

= \frac{1}{4 ^{2}}

= 2 \cdot \frac{1}{4 ^{2}}

分式相乘:

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

= \frac{1 \cdot 2}{4 ^{2}}

数字相乘:

1 \cdot 2 = 2

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

约分:

2

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

2^{3} = 8

= \frac{1}{8}

= 1 - \frac{1}{8}

将项转换为分式:

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

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

1 \cdot 8 - 1 = 7

1 \cdot 8 - 1

数字相乘:

1 \cdot 8 = 8

= 8 - 1

数字相减:

8 - 1 = 7

= 7

= \frac{7}{8}

= \frac{7}{8}

流行的例子

arccos (\frac{50}{85})

cot (- \frac{9 π}{4})

tan (- \frac{1}{3})

sin (π + i \cdot \frac{π}{2})

cos (25 2^{\circ})