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受欢迎的三角函数 >

cos^2(a)= 1/2

解答

cos^{2} (a) = \frac{1}{2}

解答

a = 0.78539 \dots + 2 πn, a = 2 π - 0.78539 \dots + 2 πn, a = 2.35619 \dots + 2 πn, a = - 2.35619 \dots + 2 πn

+1

度数

a = 4 5^{\circ} + 36 0^{\circ} n, a = 31 5^{\circ} + 36 0^{\circ} n, a = 13 5^{\circ} + 36 0^{\circ} n, a = - 13 5^{\circ} + 36 0^{\circ} n

求解步骤

cos^{2} (a) = \frac{1}{2}

用替代法求解

cos^{2} (a) = \frac{1}{2}

令

: cos (a) = u

u^{2} = \frac{1}{2}

u^{2} = \frac{1}{2} : u = \frac{1}{2}, u = - \frac{1}{2}

u^{2} = \frac{1}{2}

对于

x^{2} = f (a)

解为

x = f (a), - f (a)

u = \frac{1}{2}, u = - \frac{1}{2}

u = cos (a)

代回

cos (a) = \frac{1}{2}, cos (a) = - \frac{1}{2}

cos (a) = \frac{1}{2}, cos (a) = - \frac{1}{2}

cos (a) = \frac{1}{2} : a = arccos (\frac{1}{2}) + 2 πn, a = 2 π - arccos (\frac{1}{2}) + 2 πn

cos (a) = \frac{1}{2}

使用反三角函数性质

cos (a) = \frac{1}{2}

cos (a) = \frac{1}{2}

的通解

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

a = arccos (\frac{1}{2}) + 2 πn, a = 2 π - arccos (\frac{1}{2}) + 2 πn

a = arccos (\frac{1}{2}) + 2 πn, a = 2 π - arccos (\frac{1}{2}) + 2 πn

cos (a) = - \frac{1}{2} : a = arccos (- \frac{1}{2}) + 2 πn, a = - arccos (- \frac{1}{2}) + 2 πn

cos (a) = - \frac{1}{2}

使用反三角函数性质

cos (a) = - \frac{1}{2}

cos (a) = - \frac{1}{2}

的通解

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

a = arccos (- \frac{1}{2}) + 2 πn, a = - arccos (- \frac{1}{2}) + 2 πn

a = arccos (- \frac{1}{2}) + 2 πn, a = - arccos (- \frac{1}{2}) + 2 πn

合并所有解

a = arccos (\frac{1}{2}) + 2 πn, a = 2 π - arccos (\frac{1}{2}) + 2 πn, a = arccos (- \frac{1}{2}) + 2 πn, a = - arccos (- \frac{1}{2}) + 2 πn

以小数形式表示解

a = 0.78539 \dots + 2 πn, a = 2 π - 0.78539 \dots + 2 πn, a = 2.35619 \dots + 2 πn, a = - 2.35619 \dots + 2 πn

作图

流行的例子

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