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受欢迎的三角函数 >

6sin(θ)-1=4sin(θ)

解答

6 sin (θ) - 1 = 4 sin (θ)

解答

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

+1

度数

θ = 3 0^{\circ} + 36 0^{\circ} n, θ = 15 0^{\circ} + 36 0^{\circ} n

求解步骤

6 sin (θ) - 1 = 4 sin (θ)

用替代法求解

6 sin (θ) - 1 = 4 sin (θ)

令

: sin (θ) = u

6 u - 1 = 4 u

6 u - 1 = 4 u : u = \frac{1}{2}

6 u - 1 = 4 u

将

1

到右边

6 u - 1 = 4 u

两边加上

1

6 u - 1 + 1 = 4 u + 1

化简

6 u = 4 u + 1

6 u = 4 u + 1

将

4 u

para o lado esquerdo

6 u = 4 u + 1

两边减去

4 u

6 u - 4 u = 4 u + 1 - 4 u

化简

2 u = 1

2 u = 1

两边除以

2

2 u = 1

两边除以

2

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

化简

u = \frac{1}{2}

u = \frac{1}{2}

u = sin (θ)

代回

sin (θ) = \frac{1}{2}

sin (θ) = \frac{1}{2}

sin (θ) = \frac{1}{2} : θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

sin (θ) = \frac{1}{2}

sin (θ) = \frac{1}{2}

的通解

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

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

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

合并所有解

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

作图

流行的例子

tan(x)=(sqrt(2))/4

tan (x) = \frac{2}{4}

7cos(x)+12=6cos(x)+13

7 cos (x) + 12 = 6 cos (x) + 13

sin(x/2)+cos(x/2)=sqrt(2)

sin (\frac{x}{2}) + cos (\frac{x}{2}) = 2

2tan(x)-16=0,0<= x< pi/2

2 tan (x) - 16 = 0, 0 \leq x < \frac{π}{2}

4 sec (x) + 6 = - 2