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受欢迎的三角函数 >

-2/(sqrt(3))cos(3θ)=1,0<= θ<= 2pi

解答

- \frac{2}{3} cos (3 θ) = 1, 0 \leq θ \leq 2 π

解答

θ = \frac{5 π}{18}, θ = \frac{7 π}{18}, θ = \frac{17 π}{18}, θ = \frac{19 π}{18}, θ = \frac{29 π}{18}, θ = \frac{31 π}{18}

求解步骤

- \frac{2}{3} cos (3 θ) = 1, 0 \leq θ \leq 2 π

化简

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

- \frac{2}{3}

乘以共轭根式

\frac{3}{3}

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

33 = 3

33

使用根式运算法则:

a a = a

33 = 3

= 3

= - \frac{2 3}{3}

(- \frac{2 3}{3}) cos (3 θ) = 1

在两边乘以

3

(- \frac{2 3}{3}) cos (3 θ) = 1

在两边乘以

3

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

化简

- 23 cos (3 θ) = 3

- 23 cos (3 θ) = 3

两边除以

- 23

- 23 cos (3 θ) = 3

两边除以

- 23

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

化简

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

化简

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

\frac{- 2 3 cos ( 3 θ )}{- 2 3}

使用分式法则:

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

= \frac{2 3 cos ( 3 θ )}{2 3}

数字相除:

\frac{2}{2} = 1

= \frac{3 cos ( 3 θ )}{3}

约分:

3

= cos (3 θ)

化简

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

\frac{3}{- 2 3}

使用分式法则:

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

= - \frac{3}{2 3}

使用根式运算法则:

n a = a^{\frac{1}{n}}

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

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

使用指数法则:

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

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

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

数字相减:

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

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

使用根式运算法则:

a^{\frac{1}{n}} = n a

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

= - \frac{3}{2}

cos (3 θ) = - \frac{3}{2}

cos (3 θ) = - \frac{3}{2}

cos (3 θ) = - \frac{3}{2}

cos (3 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}

3 θ = \frac{5 π}{6} + 2 πn, 3 θ = \frac{7 π}{6} + 2 πn

3 θ = \frac{5 π}{6} + 2 πn, 3 θ = \frac{7 π}{6} + 2 πn

解

3 θ = \frac{5 π}{6} + 2 πn : θ = \frac{5 π}{18} + \frac{2 πn}{3}

3 θ = \frac{5 π}{6} + 2 πn

两边除以

3

3 θ = \frac{5 π}{6} + 2 πn

两边除以

3

\frac{3 θ}{3} = \frac{\frac{5 π}{6}}{3} + \frac{2 πn}{3}

化简

\frac{3 θ}{3} = \frac{\frac{5 π}{6}}{3} + \frac{2 πn}{3}

化简

\frac{3 θ}{3} : θ

\frac{3 θ}{3}

数字相除:

\frac{3}{3} = 1

= θ

化简

\frac{\frac{5 π}{6}}{3} + \frac{2 πn}{3} : \frac{5 π}{18} + \frac{2 πn}{3}

\frac{\frac{5 π}{6}}{3} + \frac{2 πn}{3}

\frac{\frac{5 π}{6}}{3} = \frac{5 π}{18}

\frac{\frac{5 π}{6}}{3}

使用分式法则:

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

= \frac{5 π}{6 \cdot 3}

数字相乘:

6 \cdot 3 = 18

= \frac{5 π}{18}

= \frac{5 π}{18} + \frac{2 πn}{3}

θ = \frac{5 π}{18} + \frac{2 πn}{3}

θ = \frac{5 π}{18} + \frac{2 πn}{3}

θ = \frac{5 π}{18} + \frac{2 πn}{3}

解

3 θ = \frac{7 π}{6} + 2 πn : θ = \frac{7 π}{18} + \frac{2 πn}{3}

3 θ = \frac{7 π}{6} + 2 πn

两边除以

3

3 θ = \frac{7 π}{6} + 2 πn

两边除以

3

\frac{3 θ}{3} = \frac{\frac{7 π}{6}}{3} + \frac{2 πn}{3}

化简

\frac{3 θ}{3} = \frac{\frac{7 π}{6}}{3} + \frac{2 πn}{3}

化简

\frac{3 θ}{3} : θ

\frac{3 θ}{3}

数字相除:

\frac{3}{3} = 1

= θ

化简

\frac{\frac{7 π}{6}}{3} + \frac{2 πn}{3} : \frac{7 π}{18} + \frac{2 πn}{3}

\frac{\frac{7 π}{6}}{3} + \frac{2 πn}{3}

\frac{\frac{7 π}{6}}{3} = \frac{7 π}{18}

\frac{\frac{7 π}{6}}{3}

使用分式法则:

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

= \frac{7 π}{6 \cdot 3}

数字相乘:

6 \cdot 3 = 18

= \frac{7 π}{18}

= \frac{7 π}{18} + \frac{2 πn}{3}

θ = \frac{7 π}{18} + \frac{2 πn}{3}

θ = \frac{7 π}{18} + \frac{2 πn}{3}

θ = \frac{7 π}{18} + \frac{2 πn}{3}

θ = \frac{5 π}{18} + \frac{2 πn}{3}, θ = \frac{7 π}{18} + \frac{2 πn}{3}

在

0 \leq θ \leq 2 π

范围内的解

θ = \frac{5 π}{18}, θ = \frac{7 π}{18}, θ = \frac{17 π}{18}, θ = \frac{19 π}{18}, θ = \frac{29 π}{18}, θ = \frac{31 π}{18}

作图

流行的例子

8(cos(x))^2-6sin(x)=3

8 (cos (x))^{2} - 6 sin (x) = 3

sin (θ) = - \frac{5}{7}

cos(x)sin(x)=sin(x)

cos (x) sin (x) = sin (x)

sec (θ) = 8

solvefor x,2cos(2x)=0

so l v e f or x, 2 cos (2 x) = 0