TF – naloga 5 – Mate(j)matika

Naloga

a) Naj bo $\sin\alpha=\frac{3}{5}$ in $\alpha$ topi kot. Izračunaj $\cos 2\alpha$ , $\cot 2\alpha$ , $\tan 2\alpha$ , $\sin(2\alpha-\frac{\pi}{4})$ , $\cos(2\alpha-\frac{\pi}{6})$ , $\tan(\frac{2\pi}{3}+2\alpha).$

b) Naj bo $\cot\alpha=-\frac{8}{17}$ in $\alpha$ topi kot. Izračunaj $\cos 2\alpha$ , $\cot 2\alpha$ , $\sin 2\alpha$ , $\sin(2\alpha+\frac{\pi}{3})$ , $\cos(2\alpha+\frac{13\pi}{4})$ , $\cot(\frac{13\pi}{6}-2\alpha).$

c) Naj bo $\cos \alpha=\frac{24}{25}$ in $\dfrac{3\pi}{2}<\alpha<2\pi$ . Izračunaj $\cos 2\alpha$ , $\tan 2\alpha$ , $\sin 2\alpha$ , $\cos(2\alpha-\frac{5\pi}{3})$ , $\cos(2\alpha-\frac{7\pi}{6})$ , $\tan(\frac{11\pi}{3}-2\alpha).$