Oblicz sinus kąta ostrego, jeżeli tg²α-8=0
0°<α<90°
tg²α-8=0
tg²α=8
tgα=2√2
tgα=sinα/cosα
sin²α+cos²α=1
sinα=cosαtgα
sinα=2√2cosα
(2√2cosα)²+cos²α=1
8cos²α+cos²α=1
9cos²α=1
cos²α=¹/₉
cosα=¹/₃
sinα=2√2·¹/₃
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0°<α<90°
tg²α-8=0
tg²α=8
tgα=2√2
tgα=sinα/cosα
sin²α+cos²α=1
sinα=cosαtgα
sin²α+cos²α=1
sinα=2√2cosα
(2√2cosα)²+cos²α=1
sinα=2√2cosα
8cos²α+cos²α=1
sinα=2√2cosα
9cos²α=1
sinα=2√2cosα
cos²α=¹/₉
sinα=2√2cosα
cosα=¹/₃
sinα=2√2·¹/₃
cosα=¹/₃