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受欢迎的三角函数 >

(cot^2(x))/2 =3

解答

\frac{cot ^{2} ( x )}{2} = 3

解答

x = 0.38759 \dots + πn, x = 2.75399 \dots + πn

+1

度数

x = 22.20765 \dots^{\circ} + 18 0^{\circ} n, x = 157.79234 \dots^{\circ} + 18 0^{\circ} n

求解步骤

\frac{cot ^{2} ( x )}{2} = 3

用替代法求解

\frac{cot ^{2} ( x )}{2} = 3

令

: cot (x) = u

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

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

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

在两边乘以

2

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

在两边乘以

2

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

化简

u^{2} = 6

u^{2} = 6

对于

x^{2} = f (a)

解为

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

u = 6, u = - 6

u = cot (x)

代回

cot (x) = 6, cot (x) = - 6

cot (x) = 6, cot (x) = - 6

cot (x) = 6 : x = arccot (6) + πn

cot (x) = 6

使用反三角函数性质

cot (x) = 6

cot (x) = 6

的通解

cot (x) = a \Rightarrow x = arccot (a) + πn

x = arccot (6) + πn

x = arccot (6) + πn

cot (x) = - 6 : x = arccot (- 6) + πn

cot (x) = - 6

使用反三角函数性质

cot (x) = - 6

cot (x) = - 6

的通解

cot (x) = - a \Rightarrow x = arccot (- a) + πn

x = arccot (- 6) + πn

x = arccot (- 6) + πn

合并所有解

x = arccot (6) + πn, x = arccot (- 6) + πn

以小数形式表示解

x = 0.38759 \dots + πn, x = 2.75399 \dots + πn

作图

流行的例子

sin (x - 3 0^{\circ}) = 0.7

<= sqrt(3)*cos(x)-sin(x)=0

\leq 3 \cdot cos (x) - sin (x) = 0

tan^2(x)+sec^2(x)=3

tan^{2} (x) + sec^{2} (x) = 3

4sin^2(x)-6cos^2(x)=0

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sin(60-a)=0.598

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