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受欢迎的三角函数 >

5sin(x)+4=0

解答

5 sin (x) + 4 = 0

解答

x = - 0.92729 \dots + 2 πn, x = π + 0.92729 \dots + 2 πn

+1

度数

x = - 53.13010 \dots^{\circ} + 36 0^{\circ} n, x = 233.13010 \dots^{\circ} + 36 0^{\circ} n

求解步骤

5 sin (x) + 4 = 0

将

4

到右边

5 sin (x) + 4 = 0

两边减去

4

5 sin (x) + 4 - 4 = 0 - 4

化简

5 sin (x) = - 4

5 sin (x) = - 4

两边除以

5

5 sin (x) = - 4

两边除以

5

\frac{5 sin ( x )}{5} = \frac{- 4}{5}

化简

sin (x) = - \frac{4}{5}

sin (x) = - \frac{4}{5}

使用反三角函数性质

sin (x) = - \frac{4}{5}

sin (x) = - \frac{4}{5}

的通解

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

x = arcsin (- \frac{4}{5}) + 2 πn, x = π + arcsin (\frac{4}{5}) + 2 πn

x = arcsin (- \frac{4}{5}) + 2 πn, x = π + arcsin (\frac{4}{5}) + 2 πn

以小数形式表示解

x = - 0.92729 \dots + 2 πn, x = π + 0.92729 \dots + 2 πn

作图

流行的例子

tan (θ) = - \frac{7}{24}

2sin(2θ)=-sqrt(3)

2 sin (2 θ) = - 3

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tan(x+pi/4)-tan(x-pi/4)=3

tan (x + \frac{π}{4}) - tan (x - \frac{π}{4}) = 3

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