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受欢迎的三角函数 >

sin(165)sin(15)

解答

sin (16 5^{\circ}) sin (1 5^{\circ})

解答

\frac{- 3 + 2}{4}

+1

十进制

0.06698 \dots

求解步骤

sin (16 5^{\circ}) sin (1 5^{\circ})

使用三角恒等式改写:

\frac{cos ( 15 0 ^{\circ} ) - cos ( 18 0 ^{\circ} )}{2}

sin (16 5^{\circ}) sin (1 5^{\circ})

使用积化和差恒等式:

sin (s) sin (t) = \frac{1}{2} (cos (s - t) - cos (s + t))

= \frac{1}{2} (cos (16 5^{\circ} - 1 5^{\circ}) - cos (16 5^{\circ} + 1 5^{\circ}))

化简

= \frac{cos ( 15 0 ^{\circ} ) - cos ( 18 0 ^{\circ} )}{2}

= \frac{cos ( 15 0 ^{\circ} ) - cos ( 18 0 ^{\circ} )}{2}

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:

cos (18 0^{\circ}) = (- 1)

cos (18 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}

= (- 1)

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

化简

\frac{- \frac{3}{2} - ( - 1 )}{2} : \frac{- 3 + 2}{4}

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

使用法则

- (- a) = a

= \frac{- \frac{3}{2} + 1}{2}

化简

- \frac{3}{2} + 1 : \frac{- 3 + 2}{2}

- \frac{3}{2} + 1

将项转换为分式:

1 = \frac{1 \cdot 2}{2}

= - \frac{3}{2} + \frac{1 \cdot 2}{2}

因为分母相等，所以合并分式:

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

= \frac{- 3 + 1 \cdot 2}{2}

数字相乘:

1 \cdot 2 = 2

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

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

使用分式法则:

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

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

数字相乘:

2 \cdot 2 = 4

= \frac{- 3 + 2}{4}

= \frac{- 3 + 2}{4}

流行的例子

sqrt((1+cos(210))/2)

\frac{1 + cos ( 21 0 ^{\circ} )}{2}

2 sin (\frac{5 π}{2})

arcsec (\frac{1}{3})

sin (26.56 5^{\circ})

arcsin (0.259)