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受欢迎的三角函数 >

25tan^2(θ)-4=0

解答

25 tan^{2} (θ) - 4 = 0

解答

θ = 0.38050 \dots + πn, θ = - 0.38050 \dots + πn

+1

度数

θ = 21.80140 \dots^{\circ} + 18 0^{\circ} n, θ = - 21.80140 \dots^{\circ} + 18 0^{\circ} n

求解步骤

25 tan^{2} (θ) - 4 = 0

用替代法求解

25 tan^{2} (θ) - 4 = 0

令

: tan (θ) = u

25 u^{2} - 4 = 0

25 u^{2} - 4 = 0 : u = \frac{2}{5}, u = - \frac{2}{5}

25 u^{2} - 4 = 0

将

4

到右边

25 u^{2} - 4 = 0

两边加上

4

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

化简

25 u^{2} = 4

25 u^{2} = 4

两边除以

25

25 u^{2} = 4

两边除以

25

\frac{25 u ^{2}}{25} = \frac{4}{25}

化简

u^{2} = \frac{4}{25}

u^{2} = \frac{4}{25}

对于

x^{2} = f (a)

解为

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

u = \frac{4}{25}, u = - \frac{4}{25}

\frac{4}{25} = \frac{2}{5}

\frac{4}{25}

使用根式运算法则:

n \frac{a}{b} = \frac{n a}{n b},

假定

a \geq 0, b \geq 0

= \frac{4}{25}

25 = 5

25

因式分解数字:

25 = 5^{2}

= 5^{2}

使用根式运算法则:

n a^{n} = a

5^{2} = 5

= 5

= \frac{4}{5}

4 = 2

4

因式分解数字:

4 = 2^{2}

= 2^{2}

使用根式运算法则:

n a^{n} = a

2^{2} = 2

= 2

= \frac{2}{5}

- \frac{4}{25} = - \frac{2}{5}

- \frac{4}{25}

化简

\frac{4}{25} : \frac{2}{5}

\frac{4}{25}

使用根式运算法则:

n \frac{a}{b} = \frac{n a}{n b},

假定

a \geq 0, b \geq 0

= \frac{4}{25}

25 = 5

25

因式分解数字:

25 = 5^{2}

= 5^{2}

使用根式运算法则:

n a^{n} = a

5^{2} = 5

= 5

= \frac{4}{5}

4 = 2

4

因式分解数字:

4 = 2^{2}

= 2^{2}

使用根式运算法则:

n a^{n} = a

2^{2} = 2

= 2

= \frac{2}{5}

= - \frac{2}{5}

u = \frac{2}{5}, u = - \frac{2}{5}

u = tan (θ)

代回

tan (θ) = \frac{2}{5}, tan (θ) = - \frac{2}{5}

tan (θ) = \frac{2}{5}, tan (θ) = - \frac{2}{5}

tan (θ) = \frac{2}{5} : θ = arctan (\frac{2}{5}) + πn

tan (θ) = \frac{2}{5}

使用反三角函数性质

tan (θ) = \frac{2}{5}

tan (θ) = \frac{2}{5}

的通解

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

θ = arctan (\frac{2}{5}) + πn

θ = arctan (\frac{2}{5}) + πn

tan (θ) = - \frac{2}{5} : θ = arctan (- \frac{2}{5}) + πn

tan (θ) = - \frac{2}{5}

使用反三角函数性质

tan (θ) = - \frac{2}{5}

tan (θ) = - \frac{2}{5}

的通解

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

θ = arctan (- \frac{2}{5}) + πn

θ = arctan (- \frac{2}{5}) + πn

合并所有解

θ = arctan (\frac{2}{5}) + πn, θ = arctan (- \frac{2}{5}) + πn

以小数形式表示解

θ = 0.38050 \dots + πn, θ = - 0.38050 \dots + πn

作图

流行的例子

tan (x) = \frac{8}{15}

sin (θ) = - \frac{12}{13}

sin(x)cos(x)=-1/4

sin (x) cos (x) = - \frac{1}{4}

sec^{2} (θ) - 9 = 0

2cos^2(θ)=2-sin(θ)

2 cos^{2} (θ) = 2 - sin (θ)