Oblicz wartości pozostałych funkcji trygonometrycznych kata ostergo α: a) tgα = 1/4 tg=1/ctg 1/4=1/ctg ctgα=4 tgα=sinα/cosα 1/4=sinα/cosα 4sinα=cosα cosα+(4cosα)²=1 cos²α+16cosα=1 17cos²α=1 cosα=1/17 cosα=√(1/17)=1/√17=√17/17 to sinα=4√17/17 b) tgα = 50 ctg=1/tg=1/50 tgα=sinα/cosα 50=sinα/cosα sinα=50cosα (50cosα)²+cos²α=1 cos²α+2500cos²α=1 2501cos²α=1 cosα=√(1/2501)=√2501/2501 sinα=50√(2501)/2501 c) tgα = √2 sinα/cosα=√2 sinα=√2·cosα (√2cosα)²+cos²α=1 2cos²α+cos²α=1 3cos²α=1 cos²α=1/3 cosα=√(1/3)=√3/3 to sinα=√2·√3/3=√6/3 ctgα=1/tgα=1/√2=√2/2 d) sinα = 1/3 (1/3)²+cos²α=1 cos²α=1-1/9 cos²α=8/9 cosα=√(8/9)=2√2/3 tgα=1/3 :2√2/3=1/3·3/2√2=1/2√2=√2/4 ctgα=2√2/3 :1/3=2√2/3 ·3=2√2 e) cosα = 2/5 (2/5)²+sin²α=1 4/25+sin²α=1 sin²α=1-4/25 sin²α=21/25 sinα=√(21/25)=√21/5 tgα=√21/5 :2/5=√21/5 ·5/2√21/2 ctgα=2/5:√21/5=2/5·5/√21=1/√21=2√21/21 f) sinα = √2/3 (√2/3)²+cos²α=1 2/9+cos²α=1 cos²α=1-2/9 cos²α=7/9 cosα=√(7/9)=√7/3 tgα=√2/3 :√7/3=√2/3 ·3/√7=√2/√7=√14/7 ctgα=1/tgα=1 /(√14/7)=1·7/√14=7/√14=7√14/14=√14/2 g)cosα=√3/2 (√3/2)²+sin²α=1 3/4+sin²α=1 sin²α=1-3/4 sin²α=1/4 sinα=√(1/4)=1/2 tgα=(1/2)/(√3/2)=1/2 ·2/√3=1/√3=√3/3 ctgα=√3/2 :1/2=√3/2 ·2=√3
rozwiazania w zalaczniku, licze na naj nie pisalem ujemnych bokow bo wiadomo, ze bok nie moze byc ujemny
