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受欢迎的三角函数 >

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

解答

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

解答

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

+1

度数

x = 14.47751 \dots^{\circ} + 36 0^{\circ} n, x = 165.52248 \dots^{\circ} + 36 0^{\circ} n

求解步骤

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

用替代法求解

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

令

: sin (x) = u

3 u - 2 = 7 u - 3

3 u - 2 = 7 u - 3 : u = \frac{1}{4}

3 u - 2 = 7 u - 3

将

2

到右边

3 u - 2 = 7 u - 3

两边加上

2

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

化简

3 u = 7 u - 1

3 u = 7 u - 1

将

7 u

para o lado esquerdo

3 u = 7 u - 1

两边减去

7 u

3 u - 7 u = 7 u - 1 - 7 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 (x)

代回

sin (x) = \frac{1}{4}

sin (x) = \frac{1}{4}

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

sin (x) = \frac{1}{4}

使用反三角函数性质

sin (x) = \frac{1}{4}

sin (x) = \frac{1}{4}

的通解

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

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

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

合并所有解

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

以小数形式表示解

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

作图

流行的例子

55^2=50^2+90^2-2*50*90*cos(x)

5 5^{2} = 5 0^{2} + 9 0^{2} - 2 \cdot 50 \cdot 90 \cdot cos (x)

solvefor x,z=sin(2x+y)

so l v e f or x, z = sin (2 x + y)

7tan(x)=2sqrt(3)+tan(x),0<= θ<= 90

7 tan (x) = 23 + tan (x), 0^{\circ} \leq θ \leq 9 0^{\circ}

sin (X) = 1

solvefor x,(17)/(sin(x))=(23)/(sin(75))

so l v e f or x, \frac{17}{sin ( x )} = \frac{23}{sin ( 7 5 ^{\circ} )}