Matematică
MateiBoss
2015-11-10 09:00:24
cosx=3/5 xE[0, pi/2] ctgx=?
Răspunsuri la întrebare
claramaria
2015-11-10 13:04:57

[latex]cos ext{x} = dfrac{3}{5},quad ext{x}in Big[0,dfrac{pi}{2}Big]\ \ sin^2 ext{x} = 1-cos^2 ext{x} Rightarrow \ \ Rightarrow sin^2 ext{x} = 1-Big(dfrac{3}{5}Big)^2 Rightarrow \ \ Rightarrow sin^2 ext{x} = 1 - dfrac{9}{25} Rightarrow \ \ Rightarrow sin^2 ext{x}= dfrac{16}{25} Rightarrow sin ext{x} = pmdfrac{4}{5},$ dar, $ ext{x}in Big[0,dfrac{pi}{2}Big] Rightarrow \ \ [/latex] [latex]Rightarrow sin ext{x} = dfrac{4}{5} \ ext{ctg x} = dfrac{cos ext{x}}{sin ext{x}} =dfrac{dfrac{3}{5}}{dfrac{4}{5}} = dfrac{3}{4} \ Rightarrow oxed{ ext{ctg x} = dfrac{3}{4}}[/latex]

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