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受欢迎的三角函数 >

6sin(A)+3=4sin(A)+4

解答

6 sin (A) + 3 = 4 sin (A) + 4

解答

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

+1

度数

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

求解步骤

6 sin (A) + 3 = 4 sin (A) + 4

用替代法求解

6 sin (A) + 3 = 4 sin (A) + 4

令

: sin (A) = u

6 u + 3 = 4 u + 4

6 u + 3 = 4 u + 4 : u = \frac{1}{2}

6 u + 3 = 4 u + 4

将

3

到右边

6 u + 3 = 4 u + 4

两边减去

3

6 u + 3 - 3 = 4 u + 4 - 3

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 (A)

代回

sin (A) = \frac{1}{2}

sin (A) = \frac{1}{2}

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

sin (A) = \frac{1}{2}

sin (A) = \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}

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

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

合并所有解

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

作图

流行的例子

solvefor a,-10=sin(a)+15.2cos(a)

so l v e f or a, - 10 = sin (a) + 15.2 cos (a)

0=-6sin^2(θ)+3sin(θ)+2

0 = - 6 sin^{2} (θ) + 3 sin (θ) + 2

sin(2x+3/pi)= 1/2

sin (2 x + \frac{3}{π}) = \frac{1}{2}

sqrt(3)cot(x/3)+1=0

3 cot (\frac{x}{3}) + 1 = 0

sin (x) = 0.1115