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受欢迎的三角函数 >

cos(2arcsin(1/3))

解答

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

解答

\frac{7}{9}

+1

十进制

0.77777 \dots

求解步骤

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

使用三角恒等式改写:

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

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

使用倍角公式:

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

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

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

使用三角恒等式改写:

sin (arcsin (\frac{1}{3})) = \frac{1}{3}

利用以下特性:

sin (arcsin (x)) = x

= \frac{1}{3}

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

化简

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

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

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}

= 1 - \frac{2}{9}

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

数字相减:

9 - 2 = 7

= 7

= \frac{7}{9}

= \frac{7}{9}

流行的例子

(sin(pi/4))/(cos(pi/4))

\frac{sin ( \frac{π}{4} )}{cos ( \frac{π}{4} )}

arccot (\frac{4}{3})

tan((5pi)/6+(5pi)/4)

tan (\frac{5 π}{6} + \frac{5 π}{4})

cos (12 0^{\circ} - 4 5^{\circ})

arccos (0.866)