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受欢迎的三角函数 >

6cos^2(x)-4=0

解答

6 cos^{2} (x) - 4 = 0

解答

x = 0.61547 \dots + 2 πn, x = 2 π - 0.61547 \dots + 2 πn, x = 2.52611 \dots + 2 πn, x = - 2.52611 \dots + 2 πn

+1

度数

x = 35.26438 \dots^{\circ} + 36 0^{\circ} n, x = 324.73561 \dots^{\circ} + 36 0^{\circ} n, x = 144.73561 \dots^{\circ} + 36 0^{\circ} n, x = - 144.73561 \dots^{\circ} + 36 0^{\circ} n

求解步骤

6 cos^{2} (x) - 4 = 0

用替代法求解

6 cos^{2} (x) - 4 = 0

令

: cos (x) = u

6 u^{2} - 4 = 0

6 u^{2} - 4 = 0 : u = \frac{2}{3}, u = - \frac{2}{3}

6 u^{2} - 4 = 0

将

4

到右边

6 u^{2} - 4 = 0

两边加上

4

6 u^{2} - 4 + 4 = 0 + 4

化简

6 u^{2} = 4

6 u^{2} = 4

两边除以

6

6 u^{2} = 4

两边除以

6

\frac{6 u ^{2}}{6} = \frac{4}{6}

化简

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

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

对于

x^{2} = f (a)

解为

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

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

u = cos (x)

代回

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

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

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

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

使用反三角函数性质

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

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

的通解

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

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

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

cos (x) = - \frac{2}{3} : x = arccos (- \frac{2}{3}) + 2 πn, x = - arccos (- \frac{2}{3}) + 2 πn

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

使用反三角函数性质

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

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

的通解

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

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

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

合并所有解

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

以小数形式表示解

x = 0.61547 \dots + 2 πn, x = 2 π - 0.61547 \dots + 2 πn, x = 2.52611 \dots + 2 πn, x = - 2.52611 \dots + 2 πn

作图

流行的例子

csc (x) = 3.5

sin(x)=0,sin(x)=0

sin (x) = 0, sin (x) = 0

cos(x)=-7/9 , pi/2 <x<pi

cos (x) = - \frac{7}{9}, \frac{π}{2} < x < π

solvefor y,x+arctan(y/x)=0

so l v e f or y, x + arctan (\frac{y}{x}) = 0

sin(45+2α)=(sqrt(3))/2

sin (45 + 2 α) = \frac{3}{2}