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受欢迎的三角函数 >

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

解答

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

解答

\frac{5}{10} - \frac{15}{5}

+1

十进制

- 0.55098 \dots

求解步骤

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

利用以下特性:

arctan (- x) = - arctan (x)

arctan (- 2) = - arctan (2)

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

使用三角恒等式改写:

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

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

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

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

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 (2)) = \frac{5}{5}

cos (arctan (2))

使用三角恒等式改写:

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

利用以下特性:

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

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

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

化简

= \frac{5}{5}

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 (2)) = \frac{2 5}{5}

sin (arctan (2))

使用三角恒等式改写:

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

利用以下特性:

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

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

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

化简

= \frac{2 5}{5}

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

化简

\frac{1}{2} \cdot \frac{5}{5} - \frac{3}{2} \cdot \frac{2 5}{5} : \frac{5}{10} - \frac{15}{5}

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

\frac{1}{2} \cdot \frac{5}{5} = \frac{5}{10}

\frac{1}{2} \cdot \frac{5}{5}

分式相乘:

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

= \frac{1 \cdot 5}{2 \cdot 5}

乘以:

1 \cdot 5 = 5

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

数字相乘:

2 \cdot 5 = 10

= \frac{5}{10}

\frac{3}{2} \cdot \frac{2 5}{5} = \frac{15}{5}

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

分式相乘:

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

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

约分:

2

= \frac{3 5}{5}

化简

35 : 15

35

使用根式运算法则:

a b = a \cdot b

35 = 3 \cdot 5

= 3 \cdot 5

数字相乘:

3 \cdot 5 = 15

= 15

= \frac{15}{5}

= \frac{5}{10} - \frac{15}{5}

= \frac{5}{10} - \frac{15}{5}

流行的例子

60 cos (5 0^{\circ})

sin (\frac{π}{3} - \frac{π}{4})

arcsin (\frac{12}{20})

cos (- \frac{17 π}{3})

cos (\frac{7 π}{5})