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受欢迎的三角函数 >

sin(7.07t)=0.5

解答

sin (7.07 t) = 0.5

解答

t = \frac{50 π}{2121} + \frac{200 πn}{707}, t = \frac{250 π}{2121} + \frac{200 πn}{707}

度数

t = 4.24328 \dots^{\circ} + 50.91937 \dots^{\circ} n, t = 21.21640 \dots^{\circ} + 50.91937 \dots^{\circ} n

求解步骤

sin (7.07 t) = 0.5

sin (7.07 t) = 0.5

的通解

sin (x)

周期表（周期为

2 πn

"）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

7.07 t = \frac{π}{6} + 2 πn, 7.07 t = \frac{5 π}{6} + 2 πn

7.07 t = \frac{π}{6} + 2 πn, 7.07 t = \frac{5 π}{6} + 2 πn

解

7.07 t = \frac{π}{6} + 2 πn : t = \frac{50 π}{2121} + \frac{200 πn}{707}

7.07 t = \frac{π}{6} + 2 πn

在两边乘以

100

7.07 t = \frac{π}{6} + 2 πn

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

2

digits to the right of the decimal point, therefore multiply by

100

7.07 t \cdot 100 = \frac{π}{6} \cdot 100 + 2 πn \cdot 100

整理后得

707 t = \frac{50 π}{3} + 200 πn

707 t = \frac{50 π}{3} + 200 πn

两边除以

707

707 t = \frac{50 π}{3} + 200 πn

两边除以

707

\frac{707 t}{707} = \frac{\frac{50 π}{3}}{707} + \frac{200 πn}{707}

化简

\frac{707 t}{707} = \frac{\frac{50 π}{3}}{707} + \frac{200 πn}{707}

化简

\frac{707 t}{707} : t

\frac{707 t}{707}

数字相除:

\frac{707}{707} = 1

= t

化简

\frac{\frac{50 π}{3}}{707} + \frac{200 πn}{707} : \frac{50 π}{2121} + \frac{200 πn}{707}

\frac{\frac{50 π}{3}}{707} + \frac{200 πn}{707}

\frac{\frac{50 π}{3}}{707} = \frac{50 π}{2121}

\frac{\frac{50 π}{3}}{707}

使用分式法则:

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

= \frac{50 π}{3 \cdot 707}

数字相乘:

3 \cdot 707 = 2121

= \frac{50 π}{2121}

= \frac{50 π}{2121} + \frac{200 πn}{707}

t = \frac{50 π}{2121} + \frac{200 πn}{707}

t = \frac{50 π}{2121} + \frac{200 πn}{707}

t = \frac{50 π}{2121} + \frac{200 πn}{707}

解

7.07 t = \frac{5 π}{6} + 2 πn : t = \frac{250 π}{2121} + \frac{200 πn}{707}

7.07 t = \frac{5 π}{6} + 2 πn

在两边乘以

100

7.07 t = \frac{5 π}{6} + 2 πn

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

2

digits to the right of the decimal point, therefore multiply by

100

7.07 t \cdot 100 = \frac{5 π}{6} \cdot 100 + 2 πn \cdot 100

整理后得

707 t = \frac{250 π}{3} + 200 πn

707 t = \frac{250 π}{3} + 200 πn

两边除以

707

707 t = \frac{250 π}{3} + 200 πn

两边除以

707

\frac{707 t}{707} = \frac{\frac{250 π}{3}}{707} + \frac{200 πn}{707}

化简

\frac{707 t}{707} = \frac{\frac{250 π}{3}}{707} + \frac{200 πn}{707}

化简

\frac{707 t}{707} : t

\frac{707 t}{707}

数字相除:

\frac{707}{707} = 1

= t

化简

\frac{\frac{250 π}{3}}{707} + \frac{200 πn}{707} : \frac{250 π}{2121} + \frac{200 πn}{707}

\frac{\frac{250 π}{3}}{707} + \frac{200 πn}{707}

\frac{\frac{250 π}{3}}{707} = \frac{250 π}{2121}

\frac{\frac{250 π}{3}}{707}

使用分式法则:

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

= \frac{250 π}{3 \cdot 707}

数字相乘:

3 \cdot 707 = 2121

= \frac{250 π}{2121}

= \frac{250 π}{2121} + \frac{200 πn}{707}

t = \frac{250 π}{2121} + \frac{200 πn}{707}

t = \frac{250 π}{2121} + \frac{200 πn}{707}

t = \frac{250 π}{2121} + \frac{200 πn}{707}

t = \frac{50 π}{2121} + \frac{200 πn}{707}, t = \frac{250 π}{2121} + \frac{200 πn}{707}

作图

流行的例子

tan(x)= 1/(sqrt(3)),0<= x<2pi

tan (x) = \frac{1}{3}, 0 \leq x < 2 π

-2sin(2x)=2pi

- 2 sin (2 x) = 2 π

arccos(θ)= 17/18

arccos (θ) = \frac{17}{18}

cos(θ)=-2/9

cos (θ) = - \frac{2}{9}

solvefor y=sin(x),x

so l v e f or y = sin (x), x