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受欢迎的三角函数 >

solvefor t,y=3sin(2t-pi/4)

解答

求解

t, y = 3 sin (2 t - \frac{π}{4})

解答

t = \frac{arcsin ( \frac{y}{3} )}{2} + πn + \frac{π}{8}, t = πn + \frac{π}{2} + \frac{π}{8} + \frac{arcsin ( - \frac{y}{3} )}{2}

求解步骤

y = 3 sin (2 t - \frac{π}{4})

交换两边

3 sin (2 t - \frac{π}{4}) = y

两边除以

3

3 sin (2 t - \frac{π}{4}) = y

两边除以

3

\frac{3 sin ( 2 t - \frac{π}{4} )}{3} = \frac{y}{3}

化简

sin (2 t - \frac{π}{4}) = \frac{y}{3}

sin (2 t - \frac{π}{4}) = \frac{y}{3}

使用反三角函数性质

sin (2 t - \frac{π}{4}) = \frac{y}{3}

sin (2 t - \frac{π}{4}) = \frac{y}{3}

的通解

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

2 t - \frac{π}{4} = arcsin (\frac{y}{3}) + 2 πn, 2 t - \frac{π}{4} = π + arcsin (- \frac{y}{3}) + 2 πn

2 t - \frac{π}{4} = arcsin (\frac{y}{3}) + 2 πn, 2 t - \frac{π}{4} = π + arcsin (- \frac{y}{3}) + 2 πn

解

2 t - \frac{π}{4} = arcsin (\frac{y}{3}) + 2 πn : t = \frac{arcsin ( \frac{y}{3} )}{2} + πn + \frac{π}{8}

2 t - \frac{π}{4} = arcsin (\frac{y}{3}) + 2 πn

将

\frac{π}{4}

到右边

2 t - \frac{π}{4} = arcsin (\frac{y}{3}) + 2 πn

两边加上

\frac{π}{4}

2 t - \frac{π}{4} + \frac{π}{4} = arcsin (\frac{y}{3}) + 2 πn + \frac{π}{4}

化简

2 t = arcsin (\frac{y}{3}) + 2 πn + \frac{π}{4}

2 t = arcsin (\frac{y}{3}) + 2 πn + \frac{π}{4}

两边除以

2

2 t = arcsin (\frac{y}{3}) + 2 πn + \frac{π}{4}

两边除以

2

\frac{2 t}{2} = \frac{arcsin ( \frac{y}{3} )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{4}}{2}

化简

\frac{2 t}{2} = \frac{arcsin ( \frac{y}{3} )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{4}}{2}

化简

\frac{2 t}{2} : t

\frac{2 t}{2}

数字相除:

\frac{2}{2} = 1

= t

化简

\frac{arcsin ( \frac{y}{3} )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{4}}{2} : \frac{arcsin ( \frac{y}{3} )}{2} + πn + \frac{π}{8}

\frac{arcsin ( \frac{y}{3} )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{4}}{2}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

数字相除:

\frac{2}{2} = 1

= πn

\frac{\frac{π}{4}}{2} = \frac{π}{8}

\frac{\frac{π}{4}}{2}

使用分式法则:

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

= \frac{π}{4 \cdot 2}

数字相乘:

4 \cdot 2 = 8

= \frac{π}{8}

= \frac{arcsin ( \frac{y}{3} )}{2} + πn + \frac{π}{8}

t = \frac{arcsin ( \frac{y}{3} )}{2} + πn + \frac{π}{8}

t = \frac{arcsin ( \frac{y}{3} )}{2} + πn + \frac{π}{8}

t = \frac{arcsin ( \frac{y}{3} )}{2} + πn + \frac{π}{8}

解

2 t - \frac{π}{4} = π + arcsin (- \frac{y}{3}) + 2 πn : t = πn + \frac{π}{2} + \frac{π}{8} + \frac{arcsin ( - \frac{y}{3} )}{2}

2 t - \frac{π}{4} = π + arcsin (- \frac{y}{3}) + 2 πn

将

\frac{π}{4}

到右边

2 t - \frac{π}{4} = π + arcsin (- \frac{y}{3}) + 2 πn

两边加上

\frac{π}{4}

2 t - \frac{π}{4} + \frac{π}{4} = π + arcsin (- \frac{y}{3}) + 2 πn + \frac{π}{4}

化简

2 t = π + arcsin (- \frac{y}{3}) + 2 πn + \frac{π}{4}

2 t = π + arcsin (- \frac{y}{3}) + 2 πn + \frac{π}{4}

两边除以

2

2 t = π + arcsin (- \frac{y}{3}) + 2 πn + \frac{π}{4}

两边除以

2

\frac{2 t}{2} = \frac{π}{2} + \frac{arcsin ( - \frac{y}{3} )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{4}}{2}

化简

\frac{2 t}{2} = \frac{π}{2} + \frac{arcsin ( - \frac{y}{3} )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{4}}{2}

化简

\frac{2 t}{2} : t

\frac{2 t}{2}

数字相除:

\frac{2}{2} = 1

= t

化简

\frac{π}{2} + \frac{arcsin ( - \frac{y}{3} )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{4}}{2} : πn + \frac{π}{2} + \frac{π}{8} + \frac{arcsin ( - \frac{y}{3} )}{2}

\frac{π}{2} + \frac{arcsin ( - \frac{y}{3} )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{4}}{2}

对同类项分组

= \frac{π}{2} + \frac{2 πn}{2} + \frac{\frac{π}{4}}{2} + \frac{arcsin ( - \frac{y}{3} )}{2}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

数字相除:

\frac{2}{2} = 1

= πn

\frac{\frac{π}{4}}{2} = \frac{π}{8}

\frac{\frac{π}{4}}{2}

使用分式法则:

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

= \frac{π}{4 \cdot 2}

数字相乘:

4 \cdot 2 = 8

= \frac{π}{8}

= \frac{π}{2} + πn + \frac{π}{8} + \frac{arcsin ( - \frac{y}{3} )}{2}

对同类项分组

= πn + \frac{π}{2} + \frac{π}{8} + \frac{arcsin ( - \frac{y}{3} )}{2}

t = πn + \frac{π}{2} + \frac{π}{8} + \frac{arcsin ( - \frac{y}{3} )}{2}

t = πn + \frac{π}{2} + \frac{π}{8} + \frac{arcsin ( - \frac{y}{3} )}{2}

t = πn + \frac{π}{2} + \frac{π}{8} + \frac{arcsin ( - \frac{y}{3} )}{2}

t = \frac{arcsin ( \frac{y}{3} )}{2} + πn + \frac{π}{8}, t = πn + \frac{π}{2} + \frac{π}{8} + \frac{arcsin ( - \frac{y}{3} )}{2}

作图

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