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受欢迎的三角函数 >

4sec(θ)-sqrt(3)=sqrt(3)+7sec(θ)

解答

4 sec (θ) - 3 = 3 + 7 sec (θ)

解答

θ = \frac{5 π}{6} + 2 πn, θ = \frac{7 π}{6} + 2 πn

+1

度数

θ = 15 0^{\circ} + 36 0^{\circ} n, θ = 21 0^{\circ} + 36 0^{\circ} n

求解步骤

4 sec (θ) - 3 = 3 + 7 sec (θ)

用替代法求解

4 sec (θ) - 3 = 3 + 7 sec (θ)

令

: sec (θ) = u

4 u - 3 = 3 + 7 u

4 u - 3 = 3 + 7 u : u = - \frac{2 3}{3}

4 u - 3 = 3 + 7 u

将

3

到右边

4 u - 3 = 3 + 7 u

两边加上

3

4 u - 3 + 3 = 3 + 7 u + 3

化简

4 u - 3 + 3 = 3 + 7 u + 3

化简

4 u - 3 + 3 : 4 u

4 u - 3 + 3

同类项相加:

- 3 + 3 = 0

= 4 u

化简

3 + 7 u + 3 : 7 u + 23

3 + 7 u + 3

对同类项分组

= 7 u + 3 + 3

同类项相加:

3 + 3 = 23

= 7 u + 23

4 u = 7 u + 23

4 u = 7 u + 23

4 u = 7 u + 23

将

7 u

para o lado esquerdo

4 u = 7 u + 23

两边减去

7 u

4 u - 7 u = 7 u + 23 - 7 u

化简

- 3 u = 23

- 3 u = 23

两边除以

- 3

- 3 u = 23

两边除以

- 3

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

化简

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

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

u = sec (θ)

代回

sec (θ) = - \frac{2 3}{3}

sec (θ) = - \frac{2 3}{3}

sec (θ) = - \frac{2 3}{3} : θ = \frac{5 π}{6} + 2 πn, θ = \frac{7 π}{6} + 2 πn

sec (θ) = - \frac{2 3}{3}

sec (θ) = - \frac{2 3}{3}

的通解

sec (x)

周期表（周期为

2 πn

）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

θ = \frac{5 π}{6} + 2 πn, θ = \frac{7 π}{6} + 2 πn

θ = \frac{5 π}{6} + 2 πn, θ = \frac{7 π}{6} + 2 πn

合并所有解

θ = \frac{5 π}{6} + 2 πn, θ = \frac{7 π}{6} + 2 πn

作图

流行的例子

1/(sqrt(15))=cos(x)

\frac{1}{15} = cos (x)

cos^2(θ)=3sin^2(θ)

cos^{2} (θ) = 3 sin^{2} (θ)

sinh (x) = \frac{5}{4}

3 - 4 cos (A) = 1

sin (a) = - \frac{3}{5}