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受欢迎的三角函数 >

4sec(θ)+2sqrt(3)=sec(θ)

解答

4 sec (θ) + 23 = 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) + 23 = sec (θ)

用替代法求解

4 sec (θ) + 23 = sec (θ)

令

: sec (θ) = u

4 u + 23 = u

4 u + 23 = u : u = - \frac{2 3}{3}

4 u + 23 = u

将

23

到右边

4 u + 23 = u

两边减去

23

4 u + 23 - 23 = u - 23

化简

4 u = u - 23

4 u = u - 23

将

u

para o lado esquerdo

4 u = u - 23

两边减去

u

4 u - u = u - 23 - 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

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

2 cos (3 x) - 3 = 0

cos^2(x)-8cos(x)-1=0

cos^{2} (x) - 8 cos (x) - 1 = 0

cos (x) + 2 = 1

2 cos (2 θ) = - 1

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

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