cos α = 0,8 sin²α + cos² α = 1 sin² α + 0,64=1 sin² α = 0,36 sin α =0,6 tg α = sin α / cos α = 0,6 / 0,8 = 0,75 ctg α = 4/3 ------------------------- sin α = 0,4 sin²α + cos² α = 1 0,16+cos² α = 1 0,84 = cos² α cos² α = 21/25 cos α = √21 / 5 tg α = 0,4 / (√21 / 5)= 0,4* 5/√21=2/√21 = 2√21 / 21 ctg α = √21 / 2 ---------------------- tg α = 2,4 ctg α = 1 / 2,4 = 1 / (12/5) = 1 * 5/12 = 5/12 2,4 = sin α / cos α sin α =2,4 cos α sin² α + cos² α = 1 (2,4cos α)² + cos² α = 1 5,76 cos² α + cos² α = 1 6,76 cos² α = 1 169/25 cos² α = 1 cos ² α = 25/169 cos α = 5/13 sin α = 12/5 * 5/13 = 12 * 1/13=12/13
1. cosα= 0,8 [latex]x^{2}+8^{2}=10^{2} \x^{2}+64=100\ x^{2}=36\ x=6[/latex] [latex]sinalpha=frac{6}{10}=0,6\ tg alpha=frac{6}{8}=0,75\ ctgalpha=frac{8}{6}=1frac{1}{3}[/latex] 2. sinα=0,4 [latex]x^{2}+4^{2}=10^{2}\ x^{2}+16=100\ x^{2}=84\ x=sqrt{84}=sqrt{4 cdot 21}=2sqrt{21}[/latex] [latex]cosalpha=frac{2sqrt{21}}{10}=frac{sqrt{21}}{5}\ tgalpha=frac{4}{2sqrt{21}}=frac{2}{sqrt{21}}cdot frac{sqrt{21}}{sqrt{21}}=frac{2sqrt{21}}{21}\ ctgalpha=frac{2sqrt{21}}{4}=frac{sqrt{21}}{2}[/latex] 3. [latex]tgalpha=2,4=frac{12}{5}[/latex] [latex]5^{2}+12^{2}=x^{2}\ x^{2}=25+144\ x^{2}=169\ x=13[/latex] [latex]sinalpha=frac{12}{13}\ cos alpha=frac{5}{13}\ ctgalpha=frac{5}{12}[/latex]
