Odpowiedź:
[tex]sin\alpha=0.68+cos\alpha\\sin^2\alpha=(0.68+cos\alpha)^2\\sin^2\alpha=0.4624+1.36cos\alpha+cos^2\alpha\\\\0.4624+1.36cos\alpha+cos^2\alpha+cos^2\alpha=1\\2cos^2\alpha+1.36cos\alpha=0.5376\\2cos^2\alpha+1.36cos\alpha-0.5376=0\\\Delta=(1.36)^2-4*2*(-0.5376)=1.8496+4.3008=6.1504\\\sqrt{\Delta}=2.48\\[/tex]
[tex]cos\alpha_1=\frac{-1.36-2.48}{4}=\frac{3.84}4=\frac{384}{100}*\frac14=0.96\\cos\alpha_2=\frac{-1.36+2.48}4=\frac{1.12}4=\frac{112}{100}*\frac14=0.28\\sin\alpha_1=0.68+0.96=1.64 - \text{nie istnieje taki kat }\alpha\\sin\alpha_2=0.68+0.28=0.96[/tex]
[tex]tg\alpha=\frac{sin \alpha_2}{cos\alpha_2}=\frac{0.96}{0.28}\approx3.43[/tex]
Szczegółowe wyjaśnienie:
[tex]sin^2\alpha+cos^2\alpha=1\\tg\alpha=\frac{sin\alpha}{cos\alpha}[/tex]
