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受欢迎的三角函数 >

sin(arcsin(1/2)+arctan(-5))

解答

sin (arcsin (\frac{1}{2}) + arctan (- 5))

解答

\frac{26 - 5 78}{52}

+1

十进制

- 0.75114 \dots

求解步骤

sin (arcsin (\frac{1}{2}) + arctan (- 5))

利用以下特性:

arctan (- x) = - arctan (x)

arctan (- 5) = - arctan (5)

= sin (arcsin (\frac{1}{2}) - arctan (5))

使用三角恒等式改写:

sin (arcsin (\frac{1}{2})) cos (arctan (5)) - cos (arcsin (\frac{1}{2})) sin (arctan (5))

sin (arcsin (\frac{1}{2}) - arctan (5))

使用角差恒等式:

sin (s - t) = sin (s) cos (t) - cos (s) sin (t)

= sin (arcsin (\frac{1}{2})) cos (arctan (5)) - cos (arcsin (\frac{1}{2})) sin (arctan (5))

= sin (arcsin (\frac{1}{2})) cos (arctan (5)) - cos (arcsin (\frac{1}{2})) sin (arctan (5))

使用三角恒等式改写:

sin (arcsin (\frac{1}{2})) = \frac{1}{2}

利用以下特性:

sin (arcsin (x)) = x

= \frac{1}{2}

使用三角恒等式改写:

cos (arctan (5)) = \frac{26}{26}

cos (arctan (5))

使用三角恒等式改写:

cos (arctan (5)) = \frac{1 + 5 ^{2}}{1 + 5 ^{2}}

利用以下特性:

cos (arctan (x)) = \frac{1 + x ^{2}}{1 + x ^{2}}

= \frac{1 + 5 ^{2}}{1 + 5 ^{2}}

= \frac{1 + 5 ^{2}}{1 + 5 ^{2}}

化简

= \frac{26}{26}

使用三角恒等式改写:

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

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

使用三角恒等式改写:

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

利用以下特性:

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

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

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

化简

= \frac{3}{2}

使用三角恒等式改写:

sin (arctan (5)) = \frac{5 26}{26}

sin (arctan (5))

使用三角恒等式改写:

sin (arctan (5)) = \frac{5 1 + 5 ^{2}}{1 + 5 ^{2}}

利用以下特性:

sin (arctan (x)) = \frac{x 1 + x ^{2}}{1 + x ^{2}}

= \frac{5 1 + 5 ^{2}}{1 + 5 ^{2}}

= \frac{5 1 + 5 ^{2}}{1 + 5 ^{2}}

化简

= \frac{5 26}{26}

= \frac{1}{2} \cdot \frac{26}{26} - \frac{3}{2} \cdot \frac{5 26}{26}

化简

\frac{1}{2} \cdot \frac{26}{26} - \frac{3}{2} \cdot \frac{5 26}{26} : \frac{26 - 5 78}{52}

\frac{1}{2} \cdot \frac{26}{26} - \frac{3}{2} \cdot \frac{5 26}{26}

\frac{1}{2} \cdot \frac{26}{26} = \frac{26}{52}

\frac{1}{2} \cdot \frac{26}{26}

分式相乘:

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

= \frac{1 \cdot 26}{2 \cdot 26}

乘以:

1 \cdot 26 = 26

= \frac{26}{2 \cdot 26}

数字相乘:

2 \cdot 26 = 52

= \frac{26}{52}

\frac{3}{2} \cdot \frac{5 26}{26} = \frac{5 78}{52}

\frac{3}{2} \cdot \frac{5 26}{26}

分式相乘:

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

= \frac{3 \cdot 5 26}{2 \cdot 26}

数字相乘:

2 \cdot 26 = 52

= \frac{5 3 26}{52}

化简

3 \cdot 526 : 578

3 \cdot 526

使用根式运算法则:

a b = a \cdot b

326 = 3 \cdot 26

= 5 3 \cdot 26

数字相乘:

3 \cdot 26 = 78

= 578

= \frac{5 78}{52}

= \frac{26}{52} - \frac{5 78}{52}

使用法则

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

= \frac{26 - 5 78}{52}

= \frac{26 - 5 78}{52}

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