cos(θ)=-0.42,0<= θ<360

解答

cos (θ) = - 0.42, 0^{\circ} \leq θ < 36 0^{\circ}

θ = 2.00424 \dots, θ = 4.27894 \dots

求解步骤

cos (θ) = - 0.42, 0^{\circ} \leq θ < 36 0^{\circ}

使用反三角函数性质

cos (θ) = - 0.42

cos (θ) = - 0.42

的通解

cos (x) = - a \Rightarrow x = arccos (- a) + 36 0^{\circ} n, x = - arccos (- a) + 36 0^{\circ} n

θ = arccos (- 0.42) + 36 0^{\circ} n, θ = - arccos (- 0.42) + 36 0^{\circ} n

θ = arccos (- 0.42) + 36 0^{\circ} n, θ = - arccos (- 0.42) + 36 0^{\circ} n

在

0 \leq θ < 36 0^{\circ}

范围内的解

θ = 2.00424 \dots, θ = 4.27894 \dots

sin (2 x) = \frac{1}{2}, 0 < x < 2 π

4 sin^{2} (θ) + 2 cos (θ) = 3

\frac{1715}{70} = tan (4 5^{\circ} + \frac{θ}{2})

cos (3 x) = sin (x - 3 0^{\circ})

885 cos (θ) - 70 = cos (25 0^{\circ})