zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的三角函数 >

-sin(A)-1=3sin(A)+2

解答

- sin (A) - 1 = 3 sin (A) + 2

解答

A = - 0.84806 \dots + 2 πn, A = π + 0.84806 \dots + 2 πn

+1

度数

A = - 48.59037 \dots^{\circ} + 36 0^{\circ} n, A = 228.59037 \dots^{\circ} + 36 0^{\circ} n

求解步骤

- sin (A) - 1 = 3 sin (A) + 2

用替代法求解

- sin (A) - 1 = 3 sin (A) + 2

令

: sin (A) = u

- u - 1 = 3 u + 2

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

- u - 1 = 3 u + 2

将

1

到右边

- u - 1 = 3 u + 2

两边加上

1

- u - 1 + 1 = 3 u + 2 + 1

化简

- u = 3 u + 3

- u = 3 u + 3

将

3 u

para o lado esquerdo

- u = 3 u + 3

两边减去

3 u

- u - 3 u = 3 u + 3 - 3 u

化简

- 4 u = 3

- 4 u = 3

两边除以

- 4

- 4 u = 3

两边除以

- 4

\frac{- 4 u}{- 4} = \frac{3}{- 4}

化简

u = - \frac{3}{4}

u = - \frac{3}{4}

u = sin (A)

代回

sin (A) = - \frac{3}{4}

sin (A) = - \frac{3}{4}

sin (A) = - \frac{3}{4} : A = arcsin (- \frac{3}{4}) + 2 πn, A = π + arcsin (\frac{3}{4}) + 2 πn

sin (A) = - \frac{3}{4}

使用反三角函数性质

sin (A) = - \frac{3}{4}

sin (A) = - \frac{3}{4}

的通解

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

A = arcsin (- \frac{3}{4}) + 2 πn, A = π + arcsin (\frac{3}{4}) + 2 πn

A = arcsin (- \frac{3}{4}) + 2 πn, A = π + arcsin (\frac{3}{4}) + 2 πn

合并所有解

A = arcsin (- \frac{3}{4}) + 2 πn, A = π + arcsin (\frac{3}{4}) + 2 πn

以小数形式表示解

A = - 0.84806 \dots + 2 πn, A = π + 0.84806 \dots + 2 πn

作图

流行的例子

2+cos(2x)=3cos(x)

2 + cos (2 x) = 3 cos (x)

3 cot (θ) + 4 = 0

2 sin (3 θ) = 0

cot (t) = 3

3 sin (2 x) = 2