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受欢迎的三角函数 >

sin(30t)=-0.625

解答

sin (30 t) = - 0.625

解答

t = - \frac{0.67513 \dots}{30} + \frac{πn}{15}, t = \frac{π}{30} + \frac{0.67513 \dots}{30} + \frac{πn}{15}

+1

度数

t = - 1.28940 \dots^{\circ} + 1 2^{\circ} n, t = 7.28940 \dots^{\circ} + 1 2^{\circ} n

求解步骤

sin (30 t) = - 0.625

使用反三角函数性质

sin (30 t) = - 0.625

sin (30 t) = - 0.625

的通解

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

30 t = arcsin (- 0.625) + 2 πn, 30 t = π + arcsin (0.625) + 2 πn

30 t = arcsin (- 0.625) + 2 πn, 30 t = π + arcsin (0.625) + 2 πn

解

30 t = arcsin (- 0.625) + 2 πn : t = - \frac{arcsin ( \frac{5}{8} )}{30} + \frac{πn}{15}

30 t = arcsin (- 0.625) + 2 πn

化简

arcsin (- 0.625) + 2 πn : - arcsin (\frac{5}{8}) + 2 πn

arcsin (- 0.625) + 2 πn

arcsin (- 0.625) = - arcsin (\frac{5}{8})

arcsin (- 0.625)

= arcsin (- \frac{5}{8})

利用以下特性:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{5}{8}) = - arcsin (\frac{5}{8})

= - arcsin (\frac{5}{8})

= - arcsin (\frac{5}{8}) + 2 πn

30 t = - arcsin (\frac{5}{8}) + 2 πn

两边除以

30

30 t = - arcsin (\frac{5}{8}) + 2 πn

两边除以

30

\frac{30 t}{30} = - \frac{arcsin ( \frac{5}{8} )}{30} + \frac{2 πn}{30}

化简

t = - \frac{arcsin ( \frac{5}{8} )}{30} + \frac{πn}{15}

t = - \frac{arcsin ( \frac{5}{8} )}{30} + \frac{πn}{15}

解

30 t = π + arcsin (0.625) + 2 πn : t = \frac{π}{30} + \frac{arcsin ( 0.625 )}{30} + \frac{πn}{15}

30 t = π + arcsin (0.625) + 2 πn

两边除以

30

30 t = π + arcsin (0.625) + 2 πn

两边除以

30

\frac{30 t}{30} = \frac{π}{30} + \frac{arcsin ( 0.625 )}{30} + \frac{2 πn}{30}

化简

t = \frac{π}{30} + \frac{arcsin ( 0.625 )}{30} + \frac{πn}{15}

t = \frac{π}{30} + \frac{arcsin ( 0.625 )}{30} + \frac{πn}{15}

t = - \frac{arcsin ( \frac{5}{8} )}{30} + \frac{πn}{15}, t = \frac{π}{30} + \frac{arcsin ( 0.625 )}{30} + \frac{πn}{15}

以小数形式表示解

t = - \frac{0.67513 \dots}{30} + \frac{πn}{15}, t = \frac{π}{30} + \frac{0.67513 \dots}{30} + \frac{πn}{15}

作图

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