Kąt α jest bostry i sin α=¾. Oblicz ⅛+tg²α
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α < 90*
sinα = ¾
tg²α = sin²α/cos²α
sin²α = (¾)² = 9/16
sin²α+cos²α = 1
cos²α = 1-sin²α = 1 - 9/16 = 16/16 - 9/16 = 7/16
tg²α = 9/16 : 7/16 = 9/16 ·16/7 = 9/7
1/8 + tg²α = 1/8 + 9/7 = 7/56 + 72/56 = 79/56 = 1 i 23/56
sin α=¾. Oblicz ⅛+tg²α
tgα=sinα/cosα=sinα/(√1-sin²α)
tg²α=sin²α/(1-sin²α)=9/16/(7/16)=9/7
1/8+tg²α=1/8+9/7=7/56+72/56=79/56
Pozdr
Hans
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α < 90*
sinα = ¾
tg²α = sin²α/cos²α
sin²α = (¾)² = 9/16
sin²α+cos²α = 1
cos²α = 1-sin²α = 1 - 9/16 = 16/16 - 9/16 = 7/16
tg²α = 9/16 : 7/16 = 9/16 ·16/7 = 9/7
1/8 + tg²α = 1/8 + 9/7 = 7/56 + 72/56 = 79/56 = 1 i 23/56
sin α=¾. Oblicz ⅛+tg²α
tgα=sinα/cosα=sinα/(√1-sin²α)
tg²α=sin²α/(1-sin²α)=9/16/(7/16)=9/7
1/8+tg²α=1/8+9/7=7/56+72/56=79/56
Pozdr
Hans