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受欢迎的三角函数 >

sin(3x)=(-3)/4

解答

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

解答

x = - \frac{0.84806 \dots}{3} + \frac{2 πn}{3}, x = \frac{π}{3} + \frac{0.84806 \dots}{3} + \frac{2 πn}{3}

+1

度数

x = - 16.19679 \dots^{\circ} + 12 0^{\circ} n, x = 76.19679 \dots^{\circ} + 12 0^{\circ} n

求解步骤

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

使用分式法则:

\frac{- a}{b} = - \frac{a}{b}

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

使用反三角函数性质

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

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

的通解

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

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

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

解

3 x = arcsin (- \frac{3}{4}) + 2 πn : x = - \frac{arcsin ( \frac{3}{4} )}{3} + \frac{2 πn}{3}

3 x = arcsin (- \frac{3}{4}) + 2 πn

化简

arcsin (- \frac{3}{4}) + 2 πn : - arcsin (\frac{3}{4}) + 2 πn

arcsin (- \frac{3}{4}) + 2 πn

利用以下特性:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{3}{4}) = - arcsin (\frac{3}{4})

= - arcsin (\frac{3}{4}) + 2 πn

3 x = - arcsin (\frac{3}{4}) + 2 πn

两边除以

3

3 x = - arcsin (\frac{3}{4}) + 2 πn

两边除以

3

\frac{3 x}{3} = - \frac{arcsin ( \frac{3}{4} )}{3} + \frac{2 πn}{3}

化简

x = - \frac{arcsin ( \frac{3}{4} )}{3} + \frac{2 πn}{3}

x = - \frac{arcsin ( \frac{3}{4} )}{3} + \frac{2 πn}{3}

解

3 x = π + arcsin (\frac{3}{4}) + 2 πn : x = \frac{π}{3} + \frac{arcsin ( \frac{3}{4} )}{3} + \frac{2 πn}{3}

3 x = π + arcsin (\frac{3}{4}) + 2 πn

两边除以

3

3 x = π + arcsin (\frac{3}{4}) + 2 πn

两边除以

3

\frac{3 x}{3} = \frac{π}{3} + \frac{arcsin ( \frac{3}{4} )}{3} + \frac{2 πn}{3}

化简

x = \frac{π}{3} + \frac{arcsin ( \frac{3}{4} )}{3} + \frac{2 πn}{3}

x = \frac{π}{3} + \frac{arcsin ( \frac{3}{4} )}{3} + \frac{2 πn}{3}

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

以小数形式表示解

x = - \frac{0.84806 \dots}{3} + \frac{2 πn}{3}, x = \frac{π}{3} + \frac{0.84806 \dots}{3} + \frac{2 πn}{3}

作图

流行的例子

4cos(x-45)+7=10

4 cos (x - 4 5^{\circ}) + 7 = 10

cos^2(x)=3(1-sin(x))

cos^{2} (x) = 3 (1 - sin (x))

- 2 = 2 cos (3 θ)

cos (x) = \frac{4}{30}

solvefor t,x=sin(2t)+1

so l v e f or t, x = sin (2 t) + 1