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受欢迎的三角函数 >

sin(-t)= 3/10

解答

sin (- t) = \frac{3}{10}

解答

t = - 0.30469 \dots - 2 πn, t = - π + 0.30469 \dots - 2 πn

+1

度数

t = - 17.45760 \dots^{\circ} - 36 0^{\circ} n, t = - 162.54239 \dots^{\circ} - 36 0^{\circ} n

求解步骤

sin (- t) = \frac{3}{10}

使用反三角函数性质

sin (- t) = \frac{3}{10}

sin (- t) = \frac{3}{10}

的通解

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

- t = arcsin (\frac{3}{10}) + 2 πn, - t = π - arcsin (\frac{3}{10}) + 2 πn

- t = arcsin (\frac{3}{10}) + 2 πn, - t = π - arcsin (\frac{3}{10}) + 2 πn

解

- t = arcsin (\frac{3}{10}) + 2 πn : t = - arcsin (\frac{3}{10}) - 2 πn

- t = arcsin (\frac{3}{10}) + 2 πn

两边除以

- 1

- t = arcsin (\frac{3}{10}) + 2 πn

两边除以

- 1

\frac{- t}{- 1} = \frac{arcsin ( \frac{3}{10} )}{- 1} + \frac{2 πn}{- 1}

化简

\frac{- t}{- 1} = \frac{arcsin ( \frac{3}{10} )}{- 1} + \frac{2 πn}{- 1}

化简

\frac{- t}{- 1} : t

\frac{- t}{- 1}

使用分式法则:

\frac{- a}{- b} = \frac{a}{b}

= \frac{t}{1}

使用法则

\frac{a}{1} = a

= t

化简

\frac{arcsin ( \frac{3}{10} )}{- 1} + \frac{2 πn}{- 1} : - arcsin (\frac{3}{10}) - 2 πn

\frac{arcsin ( \frac{3}{10} )}{- 1} + \frac{2 πn}{- 1}

\frac{arcsin ( \frac{3}{10} )}{- 1} = - arcsin (\frac{3}{10})

\frac{arcsin ( \frac{3}{10} )}{- 1}

使用分式法则:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{arcsin ( \frac{3}{10} )}{1}

使用分式法则:

\frac{a}{1} = a

\frac{arcsin ( \frac{3}{10} )}{1} = arcsin (\frac{3}{10})

= - arcsin (\frac{3}{10})

= - arcsin (\frac{3}{10}) + \frac{2 πn}{- 1}

\frac{2 πn}{- 1} = - 2 πn

\frac{2 πn}{- 1}

使用分式法则:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{2 πn}{1}

使用法则

\frac{a}{1} = a

= - 2 πn

= - arcsin (\frac{3}{10}) - 2 πn

t = - arcsin (\frac{3}{10}) - 2 πn

t = - arcsin (\frac{3}{10}) - 2 πn

t = - arcsin (\frac{3}{10}) - 2 πn

解

- t = π - arcsin (\frac{3}{10}) + 2 πn : t = - π + arcsin (\frac{3}{10}) - 2 πn

- t = π - arcsin (\frac{3}{10}) + 2 πn

两边除以

- 1

- t = π - arcsin (\frac{3}{10}) + 2 πn

两边除以

- 1

\frac{- t}{- 1} = \frac{π}{- 1} - \frac{arcsin ( \frac{3}{10} )}{- 1} + \frac{2 πn}{- 1}

化简

\frac{- t}{- 1} = \frac{π}{- 1} - \frac{arcsin ( \frac{3}{10} )}{- 1} + \frac{2 πn}{- 1}

化简

\frac{- t}{- 1} : t

\frac{- t}{- 1}

使用分式法则:

\frac{- a}{- b} = \frac{a}{b}

= \frac{t}{1}

使用法则

\frac{a}{1} = a

= t

化简

\frac{π}{- 1} - \frac{arcsin ( \frac{3}{10} )}{- 1} + \frac{2 πn}{- 1} : - π + arcsin (\frac{3}{10}) - 2 πn

\frac{π}{- 1} - \frac{arcsin ( \frac{3}{10} )}{- 1} + \frac{2 πn}{- 1}

\frac{π}{- 1} = - π

\frac{π}{- 1}

使用分式法则:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{π}{1}

使用法则

\frac{a}{1} = a

= - π

= - π - \frac{arcsin ( \frac{3}{10} )}{- 1} + \frac{2 πn}{- 1}

\frac{arcsin ( \frac{3}{10} )}{- 1} = - arcsin (\frac{3}{10})

\frac{arcsin ( \frac{3}{10} )}{- 1}

使用分式法则:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{arcsin ( \frac{3}{10} )}{1}

使用分式法则:

\frac{a}{1} = a

\frac{arcsin ( \frac{3}{10} )}{1} = arcsin (\frac{3}{10})

= - arcsin (\frac{3}{10})

\frac{2 πn}{- 1} = - 2 πn

\frac{2 πn}{- 1}

使用分式法则:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{2 πn}{1}

使用法则

\frac{a}{1} = a

= - 2 πn

= - π - (- arcsin (\frac{3}{10})) - 2 πn

使用法则

- (- a) = a

= - π + arcsin (\frac{3}{10}) - 2 πn

t = - π + arcsin (\frac{3}{10}) - 2 πn

t = - π + arcsin (\frac{3}{10}) - 2 πn

t = - π + arcsin (\frac{3}{10}) - 2 πn

t = - arcsin (\frac{3}{10}) - 2 πn, t = - π + arcsin (\frac{3}{10}) - 2 πn

以小数形式表示解

t = - 0.30469 \dots - 2 πn, t = - π + 0.30469 \dots - 2 πn

作图

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