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受欢迎的三角函数 >

-4cos(3θ)=1

解答

- 4 cos (3 θ) = 1

解答

θ = \frac{1.82347 \dots}{3} + \frac{2 πn}{3}, θ = - \frac{1.82347 \dots}{3} + \frac{2 πn}{3}

+1

度数

θ = 34.82583 \dots^{\circ} + 12 0^{\circ} n, θ = - 34.82583 \dots^{\circ} + 12 0^{\circ} n

求解步骤

- 4 cos (3 θ) = 1

两边除以

- 4

- 4 cos (3 θ) = 1

两边除以

- 4

\frac{- 4 cos ( 3 θ )}{- 4} = \frac{1}{- 4}

化简

cos (3 θ) = - \frac{1}{4}

cos (3 θ) = - \frac{1}{4}

使用反三角函数性质

cos (3 θ) = - \frac{1}{4}

cos (3 θ) = - \frac{1}{4}

的通解

cos (x) = - a \Rightarrow x = arccos (- a) + 2 πn, x = - arccos (- a) + 2 πn

3 θ = arccos (- \frac{1}{4}) + 2 πn, 3 θ = - arccos (- \frac{1}{4}) + 2 πn

3 θ = arccos (- \frac{1}{4}) + 2 πn, 3 θ = - arccos (- \frac{1}{4}) + 2 πn

解

3 θ = arccos (- \frac{1}{4}) + 2 πn : θ = \frac{arccos ( - \frac{1}{4} )}{3} + \frac{2 πn}{3}

3 θ = arccos (- \frac{1}{4}) + 2 πn

两边除以

3

3 θ = arccos (- \frac{1}{4}) + 2 πn

两边除以

3

\frac{3 θ}{3} = \frac{arccos ( - \frac{1}{4} )}{3} + \frac{2 πn}{3}

化简

θ = \frac{arccos ( - \frac{1}{4} )}{3} + \frac{2 πn}{3}

θ = \frac{arccos ( - \frac{1}{4} )}{3} + \frac{2 πn}{3}

解

3 θ = - arccos (- \frac{1}{4}) + 2 πn : θ = - \frac{arccos ( - \frac{1}{4} )}{3} + \frac{2 πn}{3}

3 θ = - arccos (- \frac{1}{4}) + 2 πn

两边除以

3

3 θ = - arccos (- \frac{1}{4}) + 2 πn

两边除以

3

\frac{3 θ}{3} = - \frac{arccos ( - \frac{1}{4} )}{3} + \frac{2 πn}{3}

化简

θ = - \frac{arccos ( - \frac{1}{4} )}{3} + \frac{2 πn}{3}

θ = - \frac{arccos ( - \frac{1}{4} )}{3} + \frac{2 πn}{3}

θ = \frac{arccos ( - \frac{1}{4} )}{3} + \frac{2 πn}{3}, θ = - \frac{arccos ( - \frac{1}{4} )}{3} + \frac{2 πn}{3}

以小数形式表示解

θ = \frac{1.82347 \dots}{3} + \frac{2 πn}{3}, θ = - \frac{1.82347 \dots}{3} + \frac{2 πn}{3}

作图

流行的例子

960=480(1-cos(7.5x))

960 = 480 (1 - cos (7.5 x))

8 = 8 tan (θ)

2sin(2x)-3cos(x)=0

2 sin (2 x) - 3 cos (x) = 0

4cos(θ)=2cos(θ)

4 cos (θ) = 2 cos (θ)

2 cos (θ) = - 2