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受欢迎的三角函数 >

7/4 cos(3θ)-1=0

解答

\frac{7}{4} cos (3 θ) - 1 = 0

解答

θ = \frac{0.96255 \dots}{3} + \frac{2 πn}{3}, θ = \frac{2 π}{3} - \frac{0.96255 \dots}{3} + \frac{2 πn}{3}

+1

度数

θ = 18.38336 \dots^{\circ} + 12 0^{\circ} n, θ = 101.61663 \dots^{\circ} + 12 0^{\circ} n

求解步骤

\frac{7}{4} cos (3 θ) - 1 = 0

将

1

到右边

\frac{7}{4} cos (3 θ) - 1 = 0

两边加上

1

\frac{7}{4} cos (3 θ) - 1 + 1 = 0 + 1

化简

\frac{7}{4} cos (3 θ) = 1

\frac{7}{4} cos (3 θ) = 1

在两边乘以

4

\frac{7}{4} cos (3 θ) = 1

在两边乘以

4

4 \cdot \frac{7}{4} cos (3 θ) = 1 \cdot 4

化简

7 cos (3 θ) = 4

7 cos (3 θ) = 4

两边除以

7

7 cos (3 θ) = 4

两边除以

7

\frac{7 cos ( 3 θ )}{7} = \frac{4}{7}

化简

cos (3 θ) = \frac{4}{7}

cos (3 θ) = \frac{4}{7}

使用反三角函数性质

cos (3 θ) = \frac{4}{7}

cos (3 θ) = \frac{4}{7}

的通解

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

3 θ = arccos (\frac{4}{7}) + 2 πn, 3 θ = 2 π - arccos (\frac{4}{7}) + 2 πn

3 θ = arccos (\frac{4}{7}) + 2 πn, 3 θ = 2 π - arccos (\frac{4}{7}) + 2 πn

解

3 θ = arccos (\frac{4}{7}) + 2 πn : θ = \frac{arccos ( \frac{4}{7} )}{3} + \frac{2 πn}{3}

3 θ = arccos (\frac{4}{7}) + 2 πn

两边除以

3

3 θ = arccos (\frac{4}{7}) + 2 πn

两边除以

3

\frac{3 θ}{3} = \frac{arccos ( \frac{4}{7} )}{3} + \frac{2 πn}{3}

化简

θ = \frac{arccos ( \frac{4}{7} )}{3} + \frac{2 πn}{3}

θ = \frac{arccos ( \frac{4}{7} )}{3} + \frac{2 πn}{3}

解

3 θ = 2 π - arccos (\frac{4}{7}) + 2 πn : θ = \frac{2 π}{3} - \frac{arccos ( \frac{4}{7} )}{3} + \frac{2 πn}{3}

3 θ = 2 π - arccos (\frac{4}{7}) + 2 πn

两边除以

3

3 θ = 2 π - arccos (\frac{4}{7}) + 2 πn

两边除以

3

\frac{3 θ}{3} = \frac{2 π}{3} - \frac{arccos ( \frac{4}{7} )}{3} + \frac{2 πn}{3}

化简

θ = \frac{2 π}{3} - \frac{arccos ( \frac{4}{7} )}{3} + \frac{2 πn}{3}

θ = \frac{2 π}{3} - \frac{arccos ( \frac{4}{7} )}{3} + \frac{2 πn}{3}

θ = \frac{arccos ( \frac{4}{7} )}{3} + \frac{2 πn}{3}, θ = \frac{2 π}{3} - \frac{arccos ( \frac{4}{7} )}{3} + \frac{2 πn}{3}

以小数形式表示解

θ = \frac{0.96255 \dots}{3} + \frac{2 πn}{3}, θ = \frac{2 π}{3} - \frac{0.96255 \dots}{3} + \frac{2 πn}{3}

作图

流行的例子

cos(x)=sin((7pi)/6),0<= x<= 2pi

cos (x) = sin (\frac{7 π}{6}), 0 \leq x \leq 2 π

cos(2x)=((3k-3))/8

cos (2 x) = \frac{( 3 k - 3 )}{8}

1.5=2.75cos(30(x-4))+3.25

1.5 = 2.75 cos (30 (x - 4)) + 3.25

sin (x) = (\frac{5}{12})

sin (x) = \frac{97}{270}