Odpowiedź:
[tex]cos \alpha = \frac{1}{4} \\sin^{2} \alpha + cos^{2} \alpha = 1\\sin^{2} \alpha +( \frac{1}{4})^{2} = 1\\\\sin^{2} \alpha + 1/16 = 1\\sin^{2} \alpha = 15/16\\sin\alpha = \frac{\sqrt{15}}{4}\\tg\alpha = \frac{\frac{\sqrt{15} }{4} }{\frac{1}{4}} \\tg\alpha = \sqrt{15} \\[/tex]
a)2 x [tex]\frac{\sqrt{15} }{4}[/tex] + 5 x [tex]\sqrt{15}[/tex] = [tex]\frac{\sqrt{15} }{2}[/tex] + 5[tex]\sqrt{15}[/tex] = 5[tex]\frac{1}{2} \sqrt{15}[/tex]
b) [tex]\sqrt{15}[/tex] - 16 x [tex]\frac{\sqrt{15} }{4}[/tex] = [tex]\sqrt{15}[/tex] - 4[tex]\sqrt{15}[/tex] = -3[tex]\sqrt{15}[/tex]
c) 3 x 15 - 2 x 15/16 = 45 - [tex]\frac{30}{16}[/tex] = 43,125