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受欢迎的三角函数 >

tan^2(x)= 1/2

解答

tan^{2} (x) = \frac{1}{2}

解答

x = 0.61547 \dots + πn, x = - 0.61547 \dots + πn

+1

度数

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

求解步骤

tan^{2} (x) = \frac{1}{2}

用替代法求解

tan^{2} (x) = \frac{1}{2}

令

: tan (x) = u

u^{2} = \frac{1}{2}

u^{2} = \frac{1}{2} : u = \frac{1}{2}, u = - \frac{1}{2}

u^{2} = \frac{1}{2}

对于

x^{2} = f (a)

解为

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

u = \frac{1}{2}, u = - \frac{1}{2}

u = tan (x)

代回

tan (x) = \frac{1}{2}, tan (x) = - \frac{1}{2}

tan (x) = \frac{1}{2}, tan (x) = - \frac{1}{2}

tan (x) = \frac{1}{2} : x = arctan (\frac{1}{2}) + πn

tan (x) = \frac{1}{2}

使用反三角函数性质

tan (x) = \frac{1}{2}

tan (x) = \frac{1}{2}

的通解

tan (x) = a \Rightarrow x = arctan (a) + πn

x = arctan (\frac{1}{2}) + πn

x = arctan (\frac{1}{2}) + πn

tan (x) = - \frac{1}{2} : x = arctan (- \frac{1}{2}) + πn

tan (x) = - \frac{1}{2}

使用反三角函数性质

tan (x) = - \frac{1}{2}

tan (x) = - \frac{1}{2}

的通解

tan (x) = - a \Rightarrow x = arctan (- a) + πn

x = arctan (- \frac{1}{2}) + πn

x = arctan (- \frac{1}{2}) + πn

合并所有解

x = arctan (\frac{1}{2}) + πn, x = arctan (- \frac{1}{2}) + πn

以小数形式表示解

x = 0.61547 \dots + πn, x = - 0.61547 \dots + πn

作图

流行的例子

sqrt(3)cos(x)-sin(2x)=0

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

5cos^2(x)+3cos(x)=0

5 cos^{2} (x) + 3 cos (x) = 0

-2/(sqrt(3))cos(3θ)=1

- \frac{2}{3} cos (3 θ) = 1

solvefor x,y=sin(xy)

so l v e f or x, y = sin (x y)

tan(t)= 1/(sqrt(3))

tan (t) = \frac{1}{3}