zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的三角函数 >

7cos^2(x)-2=0

解答

7 cos^{2} (x) - 2 = 0

解答

x = 1.00685 \dots + 2 πn, x = 2 π - 1.00685 \dots + 2 πn, x = 2.13473 \dots + 2 πn, x = - 2.13473 \dots + 2 πn

+1

度数

x = 57.68846 \dots^{\circ} + 36 0^{\circ} n, x = 302.31153 \dots^{\circ} + 36 0^{\circ} n, x = 122.31153 \dots^{\circ} + 36 0^{\circ} n, x = - 122.31153 \dots^{\circ} + 36 0^{\circ} n

求解步骤

7 cos^{2} (x) - 2 = 0

用替代法求解

7 cos^{2} (x) - 2 = 0

令

: cos (x) = u

7 u^{2} - 2 = 0

7 u^{2} - 2 = 0 : u = \frac{2}{7}, u = - \frac{2}{7}

7 u^{2} - 2 = 0

将

2

到右边

7 u^{2} - 2 = 0

两边加上

2

7 u^{2} - 2 + 2 = 0 + 2

化简

7 u^{2} = 2

7 u^{2} = 2

两边除以

7

7 u^{2} = 2

两边除以

7

\frac{7 u ^{2}}{7} = \frac{2}{7}

化简

u^{2} = \frac{2}{7}

u^{2} = \frac{2}{7}

对于

x^{2} = f (a)

解为

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

u = \frac{2}{7}, u = - \frac{2}{7}

u = cos (x)

代回

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

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

cos (x) = \frac{2}{7} : x = arccos (\frac{2}{7}) + 2 πn, x = 2 π - arccos (\frac{2}{7}) + 2 πn

cos (x) = \frac{2}{7}

使用反三角函数性质

cos (x) = \frac{2}{7}

cos (x) = \frac{2}{7}

的通解

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

x = arccos (\frac{2}{7}) + 2 πn, x = 2 π - arccos (\frac{2}{7}) + 2 πn

x = arccos (\frac{2}{7}) + 2 πn, x = 2 π - arccos (\frac{2}{7}) + 2 πn

cos (x) = - \frac{2}{7} : x = arccos (- \frac{2}{7}) + 2 πn, x = - arccos (- \frac{2}{7}) + 2 πn

cos (x) = - \frac{2}{7}

使用反三角函数性质

cos (x) = - \frac{2}{7}

cos (x) = - \frac{2}{7}

的通解

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

x = arccos (- \frac{2}{7}) + 2 πn, x = - arccos (- \frac{2}{7}) + 2 πn

x = arccos (- \frac{2}{7}) + 2 πn, x = - arccos (- \frac{2}{7}) + 2 πn

合并所有解

x = arccos (\frac{2}{7}) + 2 πn, x = 2 π - arccos (\frac{2}{7}) + 2 πn, x = arccos (- \frac{2}{7}) + 2 πn, x = - arccos (- \frac{2}{7}) + 2 πn

以小数形式表示解

x = 1.00685 \dots + 2 πn, x = 2 π - 1.00685 \dots + 2 πn, x = 2.13473 \dots + 2 πn, x = - 2.13473 \dots + 2 πn

作图

流行的例子

tan(θ/2+pi/6)=-1

tan (\frac{θ}{2} + \frac{π}{6}) = - 1

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

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

cos (x) = - 0.3

4 cos (3 θ) = 0

2sin^2(x)+5cos(x)+1=0

2 sin^{2} (x) + 5 cos (x) + 1 = 0