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受欢迎的三角函数 >

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

解答

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

解答

x = \frac{π}{6} + \frac{πn}{3}

+1

度数

x = 3 0^{\circ} + 6 0^{\circ} n

求解步骤

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

使用三角恒等式改写

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

使用倍角公式:

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

= cos (2 \cdot 3 x)

cos (2 \cdot 3 x) = - 1

cos (2 \cdot 3 x) = - 1

的通解

cos (x)

周期表（周期为

2 πn

）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

2 \cdot 3 x = π + 2 πn

2 \cdot 3 x = π + 2 πn

解

2 \cdot 3 x = π + 2 πn : x = \frac{π}{6} + \frac{πn}{3}

2 \cdot 3 x = π + 2 πn

两边除以

6

2 \cdot 3 x = π + 2 πn

两边除以

6

\frac{2 \cdot 3 x}{6} = \frac{π}{6} + \frac{2 πn}{6}

化简

x = \frac{π}{6} + \frac{πn}{3}

x = \frac{π}{6} + \frac{πn}{3}

x = \frac{π}{6} + \frac{πn}{3}

作图

流行的例子

solvefor x,arctan(y/x)= pi/4

so l v e f or x, arctan (\frac{y}{x}) = \frac{π}{4}

sin(x)= 1/(4sin(x))

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

cos(4θ)=cos(3θ)

cos (4 θ) = cos (3 θ)

(-2sqrt(3))/3 =sec(θ)

\frac{- 2 3}{3} = sec (θ)

cot (x) = - 8