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受欢迎的三角函数 >

7sin(B)+3=sin(B)+2

解答

7 sin (B) + 3 = sin (B) + 2

解答

B = - 0.16744 \dots + 2 πn, B = π + 0.16744 \dots + 2 πn

+1

度数

B = - 9.59406 \dots^{\circ} + 36 0^{\circ} n, B = 189.59406 \dots^{\circ} + 36 0^{\circ} n

求解步骤

7 sin (B) + 3 = sin (B) + 2

用替代法求解

7 sin (B) + 3 = sin (B) + 2

令

: sin (B) = u

7 u + 3 = u + 2

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

7 u + 3 = u + 2

将

3

到右边

7 u + 3 = u + 2

两边减去

3

7 u + 3 - 3 = u + 2 - 3

化简

7 u = u - 1

7 u = u - 1

将

u

para o lado esquerdo

7 u = u - 1

两边减去

u

7 u - u = u - 1 - u

化简

6 u = - 1

6 u = - 1

两边除以

6

6 u = - 1

两边除以

6

\frac{6 u}{6} = \frac{- 1}{6}

化简

u = - \frac{1}{6}

u = - \frac{1}{6}

u = sin (B)

代回

sin (B) = - \frac{1}{6}

sin (B) = - \frac{1}{6}

sin (B) = - \frac{1}{6} : B = arcsin (- \frac{1}{6}) + 2 πn, B = π + arcsin (\frac{1}{6}) + 2 πn

sin (B) = - \frac{1}{6}

使用反三角函数性质

sin (B) = - \frac{1}{6}

sin (B) = - \frac{1}{6}

的通解

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

B = arcsin (- \frac{1}{6}) + 2 πn, B = π + arcsin (\frac{1}{6}) + 2 πn

B = arcsin (- \frac{1}{6}) + 2 πn, B = π + arcsin (\frac{1}{6}) + 2 πn

合并所有解

B = arcsin (- \frac{1}{6}) + 2 πn, B = π + arcsin (\frac{1}{6}) + 2 πn

以小数形式表示解

B = - 0.16744 \dots + 2 πn, B = π + 0.16744 \dots + 2 πn

作图

流行的例子

4 cos (x) = 3

cos(x+1/6 pi)cos(x-1/6 pi)=cos(2x)

cos (x + \frac{1}{6} π) cos (x - \frac{1}{6} π) = cos (2 x)

sin (x) = 0.731

sin (x) = 0.766

sin (x) = 0.755