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受欢迎的三角函数 >

sin(arcsin(1/4)+arctan(-5))

解答

sin (arcsin (\frac{1}{4}) + arctan (- 5))

解答

\frac{26 - 5 390}{104}

+1

十进制

- 0.90041 \dots

求解步骤

sin (arcsin (\frac{1}{4}) + arctan (- 5))

利用以下特性:

arctan (- x) = - arctan (x)

arctan (- 5) = - arctan (5)

= sin (arcsin (\frac{1}{4}) - arctan (5))

使用三角恒等式改写:

sin (arcsin (\frac{1}{4})) cos (arctan (5)) - cos (arcsin (\frac{1}{4})) sin (arctan (5))

sin (arcsin (\frac{1}{4}) - arctan (5))

使用角差恒等式:

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

= sin (arcsin (\frac{1}{4})) cos (arctan (5)) - cos (arcsin (\frac{1}{4})) sin (arctan (5))

= sin (arcsin (\frac{1}{4})) cos (arctan (5)) - cos (arcsin (\frac{1}{4})) sin (arctan (5))

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}

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}{4})) = \frac{15}{4}

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

使用三角恒等式改写:

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

利用以下特性:

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

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

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

化简

= \frac{15}{4}

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}{4} \cdot \frac{26}{26} - \frac{15}{4} \cdot \frac{5 26}{26}

化简

\frac{1}{4} \cdot \frac{26}{26} - \frac{15}{4} \cdot \frac{5 26}{26} : \frac{26 - 5 390}{104}

\frac{1}{4} \cdot \frac{26}{26} - \frac{15}{4} \cdot \frac{5 26}{26}

\frac{1}{4} \cdot \frac{26}{26} = \frac{26}{104}

\frac{1}{4} \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}{4 \cdot 26}

乘以:

1 \cdot 26 = 26

= \frac{26}{4 \cdot 26}

数字相乘:

4 \cdot 26 = 104

= \frac{26}{104}

\frac{15}{4} \cdot \frac{5 26}{26} = \frac{5 390}{104}

\frac{15}{4} \cdot \frac{5 26}{26}

分式相乘:

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

= \frac{15 \cdot 5 26}{4 \cdot 26}

数字相乘:

4 \cdot 26 = 104

= \frac{5 15 26}{104}

化简

15 \cdot 526 : 5390

15 \cdot 526

使用根式运算法则:

a b = a \cdot b

1526 = 15 \cdot 26

= 5 15 \cdot 26

数字相乘:

15 \cdot 26 = 390

= 5390

= \frac{5 390}{104}

= \frac{26}{104} - \frac{5 390}{104}

使用法则

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

= \frac{26 - 5 390}{104}

= \frac{26 - 5 390}{104}

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