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受欢迎的三角函数 >

11sin(B)+13=4sin(B)+8

解答

11 sin (B) + 13 = 4 sin (B) + 8

解答

B = - 0.79560 \dots + 2 πn, B = π + 0.79560 \dots + 2 πn

+1

度数

B = - 45.58469 \dots^{\circ} + 36 0^{\circ} n, B = 225.58469 \dots^{\circ} + 36 0^{\circ} n

求解步骤

11 sin (B) + 13 = 4 sin (B) + 8

用替代法求解

11 sin (B) + 13 = 4 sin (B) + 8

令

: sin (B) = u

11 u + 13 = 4 u + 8

11 u + 13 = 4 u + 8 : u = - \frac{5}{7}

11 u + 13 = 4 u + 8

将

13

到右边

11 u + 13 = 4 u + 8

两边减去

13

11 u + 13 - 13 = 4 u + 8 - 13

化简

11 u = 4 u - 5

11 u = 4 u - 5

将

4 u

para o lado esquerdo

11 u = 4 u - 5

两边减去

4 u

11 u - 4 u = 4 u - 5 - 4 u

化简

7 u = - 5

7 u = - 5

两边除以

7

7 u = - 5

两边除以

7

\frac{7 u}{7} = \frac{- 5}{7}

化简

u = - \frac{5}{7}

u = - \frac{5}{7}

u = sin (B)

代回

sin (B) = - \frac{5}{7}

sin (B) = - \frac{5}{7}

sin (B) = - \frac{5}{7} : B = arcsin (- \frac{5}{7}) + 2 πn, B = π + arcsin (\frac{5}{7}) + 2 πn

sin (B) = - \frac{5}{7}

使用反三角函数性质

sin (B) = - \frac{5}{7}

sin (B) = - \frac{5}{7}

的通解

sin (x) = - a \Rightarrow x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

B = arcsin (- \frac{5}{7}) + 2 πn, B = π + arcsin (\frac{5}{7}) + 2 πn

B = arcsin (- \frac{5}{7}) + 2 πn, B = π + arcsin (\frac{5}{7}) + 2 πn

合并所有解

B = arcsin (- \frac{5}{7}) + 2 πn, B = π + arcsin (\frac{5}{7}) + 2 πn

以小数形式表示解

B = - 0.79560 \dots + 2 πn, B = π + 0.79560 \dots + 2 πn

作图

流行的例子

2 = 4 cos (x)

sin (2 x + π) = 0

sin(180/2-x)=0.8

sin (\frac{180}{2} - x) = 0.8

0 = 2 cos (3 x)

2 cos (3 x) = 0