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受欢迎的三角函数 >

2(cos(150)+isin(150))

解答

2 (cos (15 0^{\circ}) + i sin (15 0^{\circ}))

解答

- 3 + i

求解步骤

2 (cos (15 0^{\circ}) + i sin (15 0^{\circ}))

使用以下普通恒等式:

cos (15 0^{\circ}) = - \frac{3}{2}

cos (15 0^{\circ})

cos (x)

周期表（周期为

36 0^{\circ} n

）：

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= - \frac{3}{2}

使用以下普通恒等式:

sin (15 0^{\circ}) = \frac{1}{2}

sin (15 0^{\circ})

sin (x)

周期表（周期为

36 0^{\circ} n

"）：

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{1}{2}

= 2 (- \frac{3}{2} + i \frac{1}{2})

化简

2 (- \frac{3}{2} + i \frac{1}{2}) : - 3 + i

2 (- \frac{3}{2} + i \frac{1}{2})

i \frac{1}{2} = \frac{i}{2}

i \frac{1}{2}

分式相乘:

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

= \frac{1 i}{2}

乘以:

1 i = i

= \frac{i}{2}

= 2 (- \frac{3}{2} + \frac{i}{2})

化简

- \frac{3}{2} + \frac{i}{2} : \frac{- 3 + i}{2}

- \frac{3}{2} + \frac{i}{2}

使用法则

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

= \frac{- 3 + i}{2}

= 2 \cdot \frac{- 3 + i}{2}

分式相乘:

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

= \frac{( - 3 + i ) \cdot 2}{2}

约分:

2

= - - 3 + i

= - 3 + i

流行的例子

(1-cos(315))/(sin(315))

\frac{1 - cos ( 31 5 ^{\circ} )}{sin ( 31 5 ^{\circ} )}

\frac{3}{sin ( 3 0 ^{\circ} )}

7(cos(120)+isin(120))

7 (cos (12 0^{\circ}) + i sin (12 0^{\circ}))

90 tan (6 3^{\circ})

arcsin(1/(sqrt(7)))

arcsin (\frac{1}{7})