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受欢迎的三角函数 >

sin(arccos(0)-arccos(1/2))

解答

sin (arccos (0) - arccos (\frac{1}{2}))

解答

\frac{1}{2}

+1

十进制

0.5

求解步骤

sin (arccos (0) - arccos (\frac{1}{2}))

使用三角恒等式改写:

arccos (0) - arccos (\frac{1}{2}) = arccos (\frac{3}{2})

arccos (0) - arccos (\frac{1}{2})

使用和差化积恒等式:

arccos (s) - arccos (t) = arccos (s t + (1 - s^{2}) (1 - t^{2}))

= arccos 0 \cdot \frac{1}{2} + (1 - 0^{2}) (1 - (\frac{1}{2})^{2})

化简:

0 \cdot \frac{1}{2} + (1 - 0^{2}) (1 - (\frac{1}{2})^{2}) = \frac{3}{2}

0 \cdot \frac{1}{2} + (1 - 0^{2}) (1 - (\frac{1}{2})^{2})

使用法则

0^{a} = 0

0^{2} = 0

= 0 \cdot \frac{1}{2} + (1 - 0) (- (\frac{1}{2})^{2} + 1)

0 \cdot \frac{1}{2} = 0

0 \cdot \frac{1}{2}

使用法则

0 \cdot a = 0

= 0

(1 - 0) (1 - (\frac{1}{2})^{2}) = \frac{3}{2}

(1 - 0) (1 - (\frac{1}{2})^{2})

数字相减:

1 - 0 = 1

= 1 \cdot (- (\frac{1}{2})^{2} + 1)

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

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

使用指数法则:

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

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

使用法则

1^{a} = 1

1^{2} = 1

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

2^{2} = 4

= \frac{1}{4}

= 1 \cdot (- \frac{1}{4} + 1)

化简

1 - \frac{1}{4} : \frac{3}{4}

1 - \frac{1}{4}

将项转换为分式:

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

= \frac{1 \cdot 4}{4} - \frac{1}{4}

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 4 - 1}{4}

1 \cdot 4 - 1 = 3

1 \cdot 4 - 1

数字相乘:

1 \cdot 4 = 4

= 4 - 1

数字相减:

4 - 1 = 3

= 3

= \frac{3}{4}

= 1 \cdot \frac{3}{4}

乘以:

1 \cdot \frac{3}{4} = \frac{3}{4}

= \frac{3}{4}

使用根式运算法则:

n \frac{a}{b} = \frac{n a}{n b},

假定

a \geq 0, b \geq 0

= \frac{3}{4}

4 = 2

4

因式分解数字:

4 = 2^{2}

= 2^{2}

使用根式运算法则:

n a^{n} = a

2^{2} = 2

= 2

= \frac{3}{2}

= 0 + \frac{3}{2}

0 + \frac{3}{2} = \frac{3}{2}

= \frac{3}{2}

= arccos (\frac{3}{2})

= sin (arccos (\frac{3}{2}))

使用三角恒等式改写:

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

利用以下特性:

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

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

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

化简

= \frac{1}{2}

流行的例子

10 tan (2 5^{\circ})

tan (3 0^{\circ} + 4 5^{\circ})

2 π cos (2 π)

arcsin (sin (3))

12 \cdot sin (4 0^{\circ})