cos(x)=(-1+sqrt(5))/4

解答

cos (x) = \frac{- 1 + 5}{4}

x = 1.25663 \dots + 2 πn, x = 2 π - 1.25663 \dots + 2 πn

度数

x = 7 2^{\circ} + 36 0^{\circ} n, x = 28 8^{\circ} + 36 0^{\circ} n

求解步骤

cos (x) = \frac{- 1 + 5}{4}

使用反三角函数性质

cos (x) = \frac{- 1 + 5}{4}

cos (x) = \frac{- 1 + 5}{4}

的通解

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

x = arccos (\frac{- 1 + 5}{4}) + 2 πn, x = 2 π - arccos (\frac{- 1 + 5}{4}) + 2 πn

x = arccos (\frac{- 1 + 5}{4}) + 2 πn, x = 2 π - arccos (\frac{- 1 + 5}{4}) + 2 πn

以小数形式表示解

x = 1.25663 \dots + 2 πn, x = 2 π - 1.25663 \dots + 2 πn

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

sin (π y) = cos (1) sin (\frac{π}{6}) - \frac{1}{2}

(2 sin (x) - 1) (cos (x) - 2) = 0

sin (a) = \frac{9}{41}

sin (x) = \frac{10}{300}