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受欢迎的三角函数 >

1/(pi^2)sin(pi(1))-((1)cos(pi(1)))/pi

解答

\frac{1}{π ^{2}} sin (π (1)) - \frac{( 1 ) cos ( π ( 1 ) )}{π}

解答

\frac{1}{π}

+1

十进制

0.31830 \dots

求解步骤

\frac{1}{π ^{2}} sin (π (1)) - \frac{( 1 ) cos ( π ( 1 ) )}{π}

= \frac{1}{π ^{2}} sin (π 1) - \frac{1 \cdot cos ( π 1 )}{π}

化简:

π 1 = π

π 1

乘以:

π 1 = π

= π

\frac{1}{π ^{2}} sin (π) - \frac{1 \cdot cos ( π )}{π} = \frac{sin ( π ) - π cos ( π )}{π ^{2}}

\frac{1}{π ^{2}} sin (π) - \frac{1 \cdot cos ( π )}{π}

\frac{1}{π ^{2}} sin (π) = \frac{sin ( π )}{π ^{2}}

\frac{1}{π ^{2}} sin (π)

分式相乘:

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

= \frac{1 \cdot sin ( π )}{π ^{2}}

乘以:

1 \cdot sin (π) = sin (π)

= \frac{sin ( π )}{π ^{2}}

\frac{1 \cdot cos ( π )}{π} = \frac{cos ( π )}{π}

\frac{1 \cdot cos ( π )}{π}

乘以:

1 \cdot cos (π) = cos (π)

= \frac{cos ( π )}{π}

= \frac{sin ( π )}{π ^{2}} - \frac{cos ( π )}{π}

π^{2}, π

的最小公倍数:

π^{2}

π^{2}, π

最小公倍数 (LCM)

计算出由出现在

π^{2}

或

π

中的因子组成的表达式

= π^{2}

根据最小公倍数调整分式

将每个分子乘以其分母转变为最小公倍数所要乘以的同一数值

π^{2}

对于

\frac{cos ( π )}{π} :

将分母和分子乘以

π

\frac{cos ( π )}{π} = \frac{cos ( π ) π}{ππ} = \frac{cos ( π ) π}{π ^{2}}

= \frac{sin ( π )}{π ^{2}} - \frac{cos ( π ) π}{π ^{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{sin ( π ) - cos ( π ) π}{π ^{2}}

= \frac{sin ( π ) - π cos ( π )}{π ^{2}}

使用以下普通恒等式:

sin (π) = 0

sin (π)

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}

= 0

使用以下普通恒等式:

cos (π) = (- 1)

cos (π)

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= (- 1)

= \frac{0 - π ( - 1 )}{π ^{2}}

化简

\frac{0 - π ( - 1 )}{π ^{2}} : \frac{1}{π}

\frac{0 - π ( - 1 )}{π ^{2}}

使用法则

- (- a) = a

= \frac{0 + π 1}{π ^{2}}

0 + π 1 = π

0 + π 1

乘以:

π 1 = π

= 0 + π

0 + π = π

= π

= \frac{π}{π ^{2}}

约分:

π

= \frac{1}{π}

= \frac{1}{π}

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