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受欢迎的三角函数 >

cos^2(x)-sin^2(x)=-3/4

解答

cos^{2} (x) - sin^{2} (x) = - \frac{3}{4}

解答

x = \frac{2.41885 \dots}{2} + πn, x = - \frac{2.41885 \dots}{2} + πn

+1

度数

x = 69.29518 \dots^{\circ} + 18 0^{\circ} n, x = - 69.29518 \dots^{\circ} + 18 0^{\circ} n

求解步骤

cos^{2} (x) - sin^{2} (x) = - \frac{3}{4}

使用三角恒等式改写

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

使用倍角公式:

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

= cos (2 x)

cos (2 x) = - \frac{3}{4}

使用反三角函数性质

cos (2 x) = - \frac{3}{4}

cos (2 x) = - \frac{3}{4}

的通解

cos (x) = - a \Rightarrow x = arccos (- a) + 2 πn, x = - arccos (- a) + 2 πn

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

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

解

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

2 x = arccos (- \frac{3}{4}) + 2 πn

两边除以

2

2 x = arccos (- \frac{3}{4}) + 2 πn

两边除以

2

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

化简

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

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

解

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

2 x = - arccos (- \frac{3}{4}) + 2 πn

两边除以

2

2 x = - arccos (- \frac{3}{4}) + 2 πn

两边除以

2

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

化简

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

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

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

以小数形式表示解

x = \frac{2.41885 \dots}{2} + πn, x = - \frac{2.41885 \dots}{2} + πn

作图

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