sin(-45), cos(-45), tg(-45), ctg(-45), arccos(sqrt(3)/2), arccos(-sqrt(3)/2), arcsin(sqrt(2)/2), arcsin(-sqrt(2)/2), arctg(1/sqrt(3)), arctg(-1/sqrt(3)), arcctg(1), arcctg(-1), Решить уравнение: cosx=1/2

Привет! Давай разберем эти тригонометрические значения и уравнения. ### Вычисления: 1. $\sin(-45^\circ) = -\frac{\sqrt{2}}{2}$ 2. $\cos(-45^\circ) = \frac{\sqrt{2}}{2}$ 3. $\text{tg}(-45^\circ) = -1$ 4. $\text{ctg}(-45^\circ) = -1$ 5. $\arccos\frac{\sqrt{3}}{2} = 30^\circ = \frac{\pi}{6}$ 6. $\arccos(-\frac{\sqrt{3}}{2}) = 150^\circ = \frac{5\pi}{6}$ 7. $\arcsin\frac{\sqrt{2}}{2} = 45^\circ = \frac{\pi}{4}$ 8. $\arcsin(-\frac{\sqrt{2}}{2}) = -45^\circ = -\frac{\pi}{4}$ 9. $\text{arctg}\frac{1}{\sqrt{3}} = 30^\circ = \frac{\pi}{6}$ 10. $\text{arctg}(-\frac{1}{\sqrt{3}}) = -30^\circ = -\frac{\pi}{6}$ 11. $\text{arcctg}(1) = 45^\circ = \frac{\pi}{4}$ 12. $\text{arcctg}(-1) = 135^\circ = \frac{3\pi}{4}$ ### Решение уравнений: Для всех уравнений $n \in \mathbb{Z}$. 1. $\cos x = \frac{1}{2} \Rightarrow x = \pm \frac{\pi}{3} + 2\pi n$ 2. $\cos x = -\frac{1}{2} \Rightarrow x = \pm \frac{2\pi}{3} + 2\pi n$ 3. $\sin x = \frac{\sqrt{3}}{2} \Rightarrow x = (-1)^n \frac{\pi}{3} + \pi n$ 4. $\sin x = -\frac{\sqrt{3}}{2} \Rightarrow x = (-1)^{n+1} \frac{\pi}{3} + \pi n$ 5. $\text{tg} x = \sqrt{3} \Rightarrow x = \frac{\pi}{3} + \pi n$ 6. $\text{tg} x = -\sqrt{3} \Rightarrow x = -\frac{\pi}{3} + \pi n$ 7. $\text{ctg} x = 1 \Rightarrow x = \frac{\pi}{4} + \pi n$ 8. $\text{ctg} x = -1 \Rightarrow x = \frac{3\pi}{4} + \pi n$ 9. $\cos(-3x) = \frac{1}{2} \Rightarrow \cos(3x) = \frac{1}{2} \Rightarrow 3x = \pm \frac{\pi}{3} + 2\pi n \Rightarrow x = \pm \frac{\pi}{9} + \frac{2\pi n}{3}$