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受欢迎的三角函数 >

-6sin(c)+0=sin(c)-3

解答

- 6 sin (c) + 0 = sin (c) - 3

解答

c = 0.44291 \dots + 2 πn, c = π - 0.44291 \dots + 2 πn

+1

度数

c = 25.37693 \dots^{\circ} + 36 0^{\circ} n, c = 154.62306 \dots^{\circ} + 36 0^{\circ} n

求解步骤

- 6 sin (c) + 0 = sin (c) - 3

用替代法求解

- 6 sin (c) + 0 = sin (c) - 3

令

: sin (c) = u

- 6 u + 0 = u - 3

- 6 u + 0 = u - 3 : u = \frac{3}{7}

- 6 u + 0 = u - 3

- 6 u + 0 = - 6 u

- 6 u = u - 3

将

u

para o lado esquerdo

- 6 u = u - 3

两边减去

u

- 6 u - u = u - 3 - u

化简

- 7 u = - 3

- 7 u = - 3

两边除以

- 7

- 7 u = - 3

两边除以

- 7

\frac{- 7 u}{- 7} = \frac{- 3}{- 7}

化简

u = \frac{3}{7}

u = \frac{3}{7}

u = sin (c)

代回

sin (c) = \frac{3}{7}

sin (c) = \frac{3}{7}

sin (c) = \frac{3}{7} : c = arcsin (\frac{3}{7}) + 2 πn, c = π - arcsin (\frac{3}{7}) + 2 πn

sin (c) = \frac{3}{7}

使用反三角函数性质

sin (c) = \frac{3}{7}

sin (c) = \frac{3}{7}

的通解

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

c = arcsin (\frac{3}{7}) + 2 πn, c = π - arcsin (\frac{3}{7}) + 2 πn

c = arcsin (\frac{3}{7}) + 2 πn, c = π - arcsin (\frac{3}{7}) + 2 πn

合并所有解

c = arcsin (\frac{3}{7}) + 2 πn, c = π - arcsin (\frac{3}{7}) + 2 πn

以小数形式表示解

c = 0.44291 \dots + 2 πn, c = π - 0.44291 \dots + 2 πn

作图

流行的例子

tan (x) = \frac{11}{12}

tan(x)cot(x)-sqrt(3)tan(x)=0

tan (x) cot (x) - 3 tan (x) = 0

cos (θ) = 0.139

1sin(30)=1.7sin(θ)

1 sin (3 0^{\circ}) = 1.7 sin (θ)

30=211.49-20.96cosh(0.03291765x)

30 = 211.49 - 20.96 cosh (0.03291765 x)