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受欢迎的三角函数 >

5sin(a)+3=sin(a)+2

解答

5 sin (a) + 3 = sin (a) + 2

解答

a = - 0.25268 \dots + 2 πn, a = π + 0.25268 \dots + 2 πn

+1

度数

a = - 14.47751 \dots^{\circ} + 36 0^{\circ} n, a = 194.47751 \dots^{\circ} + 36 0^{\circ} n

求解步骤

5 sin (a) + 3 = sin (a) + 2

用替代法求解

5 sin (a) + 3 = sin (a) + 2

令

: sin (a) = u

5 u + 3 = u + 2

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

5 u + 3 = u + 2

将

3

到右边

5 u + 3 = u + 2

两边减去

3

5 u + 3 - 3 = u + 2 - 3

化简

5 u = u - 1

5 u = u - 1

将

u

para o lado esquerdo

5 u = u - 1

两边减去

u

5 u - u = u - 1 - u

化简

4 u = - 1

4 u = - 1

两边除以

4

4 u = - 1

两边除以

4

\frac{4 u}{4} = \frac{- 1}{4}

化简

u = - \frac{1}{4}

u = - \frac{1}{4}

u = sin (a)

代回

sin (a) = - \frac{1}{4}

sin (a) = - \frac{1}{4}

sin (a) = - \frac{1}{4} : a = arcsin (- \frac{1}{4}) + 2 πn, a = π + arcsin (\frac{1}{4}) + 2 πn

sin (a) = - \frac{1}{4}

使用反三角函数性质

sin (a) = - \frac{1}{4}

sin (a) = - \frac{1}{4}

的通解

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

a = arcsin (- \frac{1}{4}) + 2 πn, a = π + arcsin (\frac{1}{4}) + 2 πn

a = arcsin (- \frac{1}{4}) + 2 πn, a = π + arcsin (\frac{1}{4}) + 2 πn

合并所有解

a = arcsin (- \frac{1}{4}) + 2 πn, a = π + arcsin (\frac{1}{4}) + 2 πn

以小数形式表示解

a = - 0.25268 \dots + 2 πn, a = π + 0.25268 \dots + 2 πn

作图

流行的例子

csc(3x)=sqrt(2)

csc (3 x) = 2

sin (x) = 0, 6

4cos^2(θ)-3=0,0<= θ<= 2pi

4 cos^{2} (θ) - 3 = 0, 0 \leq θ \leq 2 π

2sin(θ)-3=-csc(θ)

2 sin (θ) - 3 = - csc (θ)

cot (θ) = - 3