cos(x)=(sqrt(3))/3 ,0<= x<= 2pi

解答

cos (x) = \frac{3}{3}, 0 \leq x \leq 2 π

x = 0.95531 \dots, x = 2 π - 0.95531 \dots

度数

x = 54.73561 \dots^{\circ}, x = 305.26438 \dots^{\circ}

求解步骤

cos (x) = \frac{3}{3}, 0 \leq x \leq 2 π

使用反三角函数性质

cos (x) = \frac{3}{3}

cos (x) = \frac{3}{3}

的通解

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

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

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

在

0 \leq x \leq 2 π

范围内的解

x = arccos (\frac{3}{3}), x = 2 π - arccos (\frac{3}{3})

以小数形式表示解

x = 0.95531 \dots, x = 2 π - 0.95531 \dots

so l v e f or x, y = 2 sec (x)

- sin (2 x) - sin (x) = 0, 0 \leq x < 2 π

2 sin (6 x) sin (3 x) = 1 - cos (9 x)

cos (θ) sin (θ) = 172245

sec (b) cot (b) = sin (b)