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受欢迎的三角函数 >

3cos(2x)=1

解答

3 cos (2 x) = 1

解答

x = \frac{1.23095 \dots}{2} + πn, x = π - \frac{1.23095 \dots}{2} + πn

+1

度数

x = 35.26438 \dots^{\circ} + 18 0^{\circ} n, x = 144.73561 \dots^{\circ} + 18 0^{\circ} n

求解步骤

3 cos (2 x) = 1

两边除以

3

3 cos (2 x) = 1

两边除以

3

\frac{3 cos ( 2 x )}{3} = \frac{1}{3}

化简

cos (2 x) = \frac{1}{3}

cos (2 x) = \frac{1}{3}

使用反三角函数性质

cos (2 x) = \frac{1}{3}

cos (2 x) = \frac{1}{3}

的通解

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

2 x = arccos (\frac{1}{3}) + 2 πn, 2 x = 2 π - arccos (\frac{1}{3}) + 2 πn

2 x = arccos (\frac{1}{3}) + 2 πn, 2 x = 2 π - arccos (\frac{1}{3}) + 2 πn

解

2 x = arccos (\frac{1}{3}) + 2 πn : x = \frac{arccos ( \frac{1}{3} )}{2} + πn

2 x = arccos (\frac{1}{3}) + 2 πn

两边除以

2

2 x = arccos (\frac{1}{3}) + 2 πn

两边除以

2

\frac{2 x}{2} = \frac{arccos ( \frac{1}{3} )}{2} + \frac{2 πn}{2}

化简

x = \frac{arccos ( \frac{1}{3} )}{2} + πn

x = \frac{arccos ( \frac{1}{3} )}{2} + πn

解

2 x = 2 π - arccos (\frac{1}{3}) + 2 πn : x = π - \frac{arccos ( \frac{1}{3} )}{2} + πn

2 x = 2 π - arccos (\frac{1}{3}) + 2 πn

两边除以

2

2 x = 2 π - arccos (\frac{1}{3}) + 2 πn

两边除以

2

\frac{2 x}{2} = \frac{2 π}{2} - \frac{arccos ( \frac{1}{3} )}{2} + \frac{2 πn}{2}

化简

x = π - \frac{arccos ( \frac{1}{3} )}{2} + πn

x = π - \frac{arccos ( \frac{1}{3} )}{2} + πn

x = \frac{arccos ( \frac{1}{3} )}{2} + πn, x = π - \frac{arccos ( \frac{1}{3} )}{2} + πn

以小数形式表示解

x = \frac{1.23095 \dots}{2} + πn, x = π - \frac{1.23095 \dots}{2} + πn

作图

流行的例子

cos^2(x)=(1+sin(x))(1-cos(x))

cos^{2} (x) = (1 + sin (x)) (1 - cos (x))

tan(x)=1,-pi<x<= pi

tan (x) = 1, - π < x \leq π

1/(2cos^2(x-1))=(1+tan^2(x))/(2sec^2(x))

\frac{1}{2 cos ^{2} ( x - 1 )} = \frac{1 + tan ^{2} ( x )}{2 sec ^{2} ( x )}

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

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

tan(x)=(87.092)/(86.676)

tan (x) = \frac{87.092}{86.676}