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受欢迎的三角函数 >

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

解答

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

解答

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

+1

度数

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

求解步骤

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

用替代法求解

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

令

: sin (x) = 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 (x)

代回

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

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

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

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

使用反三角函数性质

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

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

的通解

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

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

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

合并所有解

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

以小数形式表示解

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

作图

流行的例子

24cos(x)=12sqrt(2)

24 cos (x) = 122

cos(3x)=(sqrt(3))/3

cos (3 x) = \frac{3}{3}

-6csc^2(x)+cot(x)=-18

- 6 csc^{2} (x) + cot (x) = - 18

tan (θ) = \frac{7}{7}

tan (2 x) = 0.75