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受欢迎的三角函数 >

sin(315-30)

解答

sin (31 5^{\circ} - 3 0^{\circ})

解答

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

+1

十进制

- 0.96592 \dots

求解步骤

sin (31 5^{\circ} - 3 0^{\circ})

化简

= sin (28 5^{\circ})

使用三角恒等式改写:

sin (15 0^{\circ}) cos (13 5^{\circ}) + cos (15 0^{\circ}) sin (13 5^{\circ})

sin (28 5^{\circ})

将

sin (28 5^{\circ})

写为

sin (15 0^{\circ} + 13 5^{\circ})

= sin (15 0^{\circ} + 13 5^{\circ})

使用角和恒等式:

sin (s + t) = sin (s) cos (t) + cos (s) sin (t)

= sin (15 0^{\circ}) cos (13 5^{\circ}) + cos (15 0^{\circ}) sin (13 5^{\circ})

= sin (15 0^{\circ}) cos (13 5^{\circ}) + cos (15 0^{\circ}) sin (13 5^{\circ})

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}

使用以下普通恒等式:

cos (13 5^{\circ}) = - \frac{2}{2}

cos (13 5^{\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{2}{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:

sin (13 5^{\circ}) = \frac{2}{2}

sin (13 5^{\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{2}{2}

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

化简

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

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

去除括号:

(- a) = - a

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

因式分解出通项

\frac{2}{2}

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

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

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

使用法则

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

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

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

分式相乘:

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

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

数字相乘:

2 \cdot 2 = 4

= \frac{2 ( - 1 - 3 )}{4}

= \frac{2 ( - 1 - 3 )}{4}

流行的例子

cot(arcsec(sqrt(17)))

cot (arcsec (17))

31 cos (4 5^{\circ})

tan(arccos(7/11))

tan (arccos (\frac{7}{11}))

(sin(80)+sin(20))/(cos(80)+cos(20))

\frac{sin ( 8 0 ^{\circ} ) + sin ( 2 0 ^{\circ} )}{cos ( 8 0 ^{\circ} ) + cos ( 2 0 ^{\circ} )}

8 cos (\frac{π}{2} + 0.1)