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受欢迎的三角函数 >

-12cos^2(θ)-8=-17

解答

- 12 cos^{2} (θ) - 8 = - 17

解答

θ = \frac{π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn, θ = \frac{7 π}{6} + 2 πn

+1

度数

θ = 3 0^{\circ} + 36 0^{\circ} n, θ = 33 0^{\circ} + 36 0^{\circ} n, θ = 15 0^{\circ} + 36 0^{\circ} n, θ = 21 0^{\circ} + 36 0^{\circ} n

求解步骤

- 12 cos^{2} (θ) - 8 = - 17

用替代法求解

- 12 cos^{2} (θ) - 8 = - 17

令

: cos (θ) = u

- 12 u^{2} - 8 = - 17

- 12 u^{2} - 8 = - 17 : u = \frac{3}{2}, u = - \frac{3}{2}

- 12 u^{2} - 8 = - 17

将

8

到右边

- 12 u^{2} - 8 = - 17

两边加上

8

- 12 u^{2} - 8 + 8 = - 17 + 8

化简

- 12 u^{2} = - 9

- 12 u^{2} = - 9

两边除以

- 12

- 12 u^{2} = - 9

两边除以

- 12

\frac{- 12 u ^{2}}{- 12} = \frac{- 9}{- 12}

化简

\frac{- 12 u ^{2}}{- 12} = \frac{- 9}{- 12}

化简

\frac{- 12 u ^{2}}{- 12} : u^{2}

\frac{- 12 u ^{2}}{- 12}

使用分式法则:

\frac{- a}{- b} = \frac{a}{b}

= \frac{12 u ^{2}}{12}

数字相除:

\frac{12}{12} = 1

= u^{2}

化简

\frac{- 9}{- 12} : \frac{3}{4}

\frac{- 9}{- 12}

使用分式法则:

\frac{- a}{- b} = \frac{a}{b}

= \frac{9}{12}

约分:

3

= \frac{3}{4}

u^{2} = \frac{3}{4}

u^{2} = \frac{3}{4}

u^{2} = \frac{3}{4}

对于

x^{2} = f (a)

解为

x = f (a), - f (a)

u = \frac{3}{4}, u = - \frac{3}{4}

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

\frac{3}{4}

使用根式运算法则:

n \frac{a}{b} = \frac{n a}{n b},

假定

a \geq 0, b \geq 0

= \frac{3}{4}

4 = 2

4

因式分解数字:

4 = 2^{2}

= 2^{2}

使用根式运算法则:

n a^{n} = a

2^{2} = 2

= 2

= \frac{3}{2}

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

- \frac{3}{4}

化简

\frac{3}{4} : \frac{3}{2}

\frac{3}{4}

使用根式运算法则:

n \frac{a}{b} = \frac{n a}{n b},

假定

a \geq 0, b \geq 0

= \frac{3}{4}

4 = 2

4

因式分解数字:

4 = 2^{2}

= 2^{2}

使用根式运算法则:

n a^{n} = a

2^{2} = 2

= 2

= \frac{3}{2}

= - \frac{3}{2}

u = \frac{3}{2}, u = - \frac{3}{2}

u = cos (θ)

代回

cos (θ) = \frac{3}{2}, cos (θ) = - \frac{3}{2}

cos (θ) = \frac{3}{2}, cos (θ) = - \frac{3}{2}

cos (θ) = \frac{3}{2} : θ = \frac{π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

cos (θ) = \frac{3}{2}

cos (θ) = \frac{3}{2}

的通解

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}

θ = \frac{π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

θ = \frac{π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

cos (θ) = - \frac{3}{2} : θ = \frac{5 π}{6} + 2 πn, θ = \frac{7 π}{6} + 2 πn

cos (θ) = - \frac{3}{2}

cos (θ) = - \frac{3}{2}

的通解

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}

θ = \frac{5 π}{6} + 2 πn, θ = \frac{7 π}{6} + 2 πn

θ = \frac{5 π}{6} + 2 πn, θ = \frac{7 π}{6} + 2 πn

合并所有解

θ = \frac{π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn, θ = \frac{7 π}{6} + 2 πn

作图

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