Wiadomo,że tangens kąta ostrego alfa jest równy . Ile wobec tego wynosi sin alfa?
tgα=sinα/cosα
tgα=sinα/√(1-sin²α)
√2/√3=sinα/√(1-sin²α)
√3sinα=√2√(1-sin²α) /²
3sin²α=√(2-2sin²α)²
3sin²α=2-2sin²α
3sin²α+2sin²α=2
5sin²α=2
sin²α=⅖
sinα=√(⅖)
sinα=√10/5
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tgα=sinα/cosα
tgα=sinα/√(1-sin²α)
√2/√3=sinα/√(1-sin²α)
√3sinα=√2√(1-sin²α) /²
3sin²α=√(2-2sin²α)²
3sin²α=2-2sin²α
3sin²α+2sin²α=2
5sin²α=2
sin²α=⅖
sinα=√(⅖)
sinα=√10/5