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受欢迎的三角函数 >

sin(2x)=0.3,-180\circ <= x<= 180

解答

sin (2 x) = 0.3, - 180 \circ \leq x \leq 18 0^{\circ}

解答

x = 0.15234 \dots, x = \frac{18 0 ^{\circ} - 0.30469 \dots}{2}, x = - 2.98924 \dots, x = \frac{- 18 0 ^{\circ} - 0.30469 \dots}{2}, x = - 6.13083 \dots, x = - 4.86473 \dots, x = - 9.27243 \dots, x = - 8.00632 \dots, x = - 12.41402 \dots, x = - 11.14792 \dots

+1

弧度

x = 0.15234 \dots, x = \frac{π - 0.30469 \dots}{2}, x = - 2.98924 \dots, x = \frac{- π - 0.30469 \dots}{2}, x = - 6.13083 \dots, x = - 4.86473 \dots, x = - 9.27243 \dots, x = - 8.00632 \dots, x = - 12.41402 \dots, x = - 11.14792 \dots

求解步骤

sin (2 x) = 0.3, - 180 \circ \leq x \leq 18 0^{\circ}

使用反三角函数性质

sin (2 x) = 0.3

sin (2 x) = 0.3

的通解

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

2 x = arcsin (0.3) + 36 0^{\circ} n, 2 x = 18 0^{\circ} - arcsin (0.3) + 36 0^{\circ} n

2 x = arcsin (0.3) + 36 0^{\circ} n, 2 x = 18 0^{\circ} - arcsin (0.3) + 36 0^{\circ} n

解

2 x = arcsin (0.3) + 36 0^{\circ} n : x = \frac{arcsin ( 0.3 )}{2} + 18 0^{\circ} n

2 x = arcsin (0.3) + 36 0^{\circ} n

两边除以

2

2 x = arcsin (0.3) + 36 0^{\circ} n

两边除以

2

\frac{2 x}{2} = \frac{arcsin ( 0.3 )}{2} + \frac{36 0 ^{\circ} n}{2}

化简

x = \frac{arcsin ( 0.3 )}{2} + 18 0^{\circ} n

x = \frac{arcsin ( 0.3 )}{2} + 18 0^{\circ} n

解

2 x = 18 0^{\circ} - arcsin (0.3) + 36 0^{\circ} n : x = 9 0^{\circ} - \frac{arcsin ( 0.3 )}{2} + 18 0^{\circ} n

2 x = 18 0^{\circ} - arcsin (0.3) + 36 0^{\circ} n

两边除以

2

2 x = 18 0^{\circ} - arcsin (0.3) + 36 0^{\circ} n

两边除以

2

\frac{2 x}{2} = 9 0^{\circ} - \frac{arcsin ( 0.3 )}{2} + \frac{36 0 ^{\circ} n}{2}

化简

x = 9 0^{\circ} - \frac{arcsin ( 0.3 )}{2} + 18 0^{\circ} n

x = 9 0^{\circ} - \frac{arcsin ( 0.3 )}{2} + 18 0^{\circ} n

x = \frac{arcsin ( 0.3 )}{2} + 18 0^{\circ} n, x = 9 0^{\circ} - \frac{arcsin ( 0.3 )}{2} + 18 0^{\circ} n

在

- 180 \circ \leq x \leq 18 0^{\circ}

范围内的解

x = 0.15234 \dots, x = \frac{18 0 ^{\circ} - 0.30469 \dots}{2}, x = - 2.98924 \dots, x = \frac{- 18 0 ^{\circ} - 0.30469 \dots}{2}, x = - 6.13083 \dots, x = - 4.86473 \dots, x = - 9.27243 \dots, x = - 8.00632 \dots, x = - 12.41402 \dots, x = - 11.14792 \dots

作图

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