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受欢迎的三角函数 >

2-4sin^2((5pi)/(12))

解答

2 - 4 sin^{2} (\frac{5 π}{12})

解答

- 3

+1

十进制

- 1.73205 \dots

求解步骤

2 - 4 sin^{2} (\frac{5 π}{12})

使用三角恒等式改写:

sin^{2} (\frac{5 π}{12}) = \frac{1 - cos ( \frac{5 π}{6} )}{2}

sin^{2} (\frac{5 π}{12})

利用以下特性:

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

使用倍角公式

cos (2 θ) = 1 - 2 sin^{2} (θ)

交换两边

2 sin^{2} (θ) - 1 = - cos (2 θ)

两边加上

1

2 sin^{2} (θ) = 1 - cos (2 θ)

两边除以

2

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

= \frac{1 - cos ( 2 \cdot \frac{5 π}{12} )}{2}

化简:

2 \cdot \frac{5 π}{12} = \frac{5 π}{6}

2 \cdot \frac{5 π}{12}

分式相乘:

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

= \frac{5 π 2}{12}

数字相乘:

5 \cdot 2 = 10

= \frac{10 π}{12}

约分:

2

= \frac{5 π}{6}

= \frac{1 - cos ( \frac{5 π}{6} )}{2}

= 2 - 4 \cdot \frac{1 - cos ( \frac{5 π}{6} )}{2}

2 - 4 \cdot \frac{1 - cos ( \frac{5 π}{6} )}{2} = 2 cos (\frac{5 π}{6})

2 - 4 \cdot \frac{1 - cos ( \frac{5 π}{6} )}{2}

4 \cdot \frac{1 - cos ( \frac{5 π}{6} )}{2} = 2 (- cos (\frac{5 π}{6}) + 1)

4 \cdot \frac{1 - cos ( \frac{5 π}{6} )}{2}

分式相乘:

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

= \frac{( 1 - cos ( \frac{5 π}{6} ) ) \cdot 4}{2}

数字相除:

\frac{4}{2} = 2

= 2 (- cos (\frac{5 π}{6}) + 1)

= 2 - 2 (- cos (\frac{5 π}{6}) + 1)

乘开

- 2 (- cos (\frac{5 π}{6}) + 1) : 2 cos (\frac{5 π}{6}) - 2

- 2 (- cos (\frac{5 π}{6}) + 1)

使用分配律:

a (b + c) = ab + a c

a = - 2, b = - cos (\frac{5 π}{6}), c = 1

= - 2 (- cos (\frac{5 π}{6})) + (- 2) \cdot 1

使用加减运算法则

- (- a) = a, + (- a) = - a

= 2 cos (\frac{5 π}{6}) - 2 \cdot 1

数字相乘:

2 \cdot 1 = 2

= 2 cos (\frac{5 π}{6}) - 2

= 2 + 2 cos (\frac{5 π}{6}) - 2

2 - 2 = 0

= 2 cos (\frac{5 π}{6})

= 2 cos (\frac{5 π}{6})

使用以下普通恒等式:

cos (\frac{5 π}{6}) = - \frac{3}{2}

cos (\frac{5 π}{6})

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}

= - \frac{3}{2}

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

化简

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

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

去除括号:

(- a) = - a

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

分式相乘:

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

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

约分:

2

= - 3

= - 3

流行的例子

sin^{2} (22. 5^{\circ})

arctan (3.7)

cos (2 \frac{5 π}{6})

cos(pi/9)cos((7pi)/(18))-sin(pi/9)sin((7pi)/(18))

cos (\frac{π}{9}) cos (\frac{7 π}{18}) - sin (\frac{π}{9}) sin (\frac{7 π}{18})

2 sin (5) cos (5)