Question

Cunoscând unul dintre numerele sin x, cos x, tangentă x cotangentă x, calculați celelalte trei numere, dacă:
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Answer 1

Răspuns:

sinx=0.6=106=53

x \: \in \: (0, \frac{\pi}{2} )x∈(0,2π)

x \: \in \: (0, \frac{\pi}{2} ) = > cadranul \: Ix∈(0,2π)=>cadranulI

{sin}^{2} x + {cos}^{2} x = 1sin2x+cos2x=1

{( \frac{3}{5} )}^{2} + {cos}^{2} x = 1(53)2+cos2x=1

\frac{9}{25} + {cos}^{2} x = 1259+cos2x=1

{cos}^{2} x = 1 - \frac{9}{25}cos2x=1−259

{cos}^{2} x = \frac{16}{25}cos2x=2516

cosx = \pm \sqrt{ \frac{16}{25} } = \pm \frac{4}{5}cosx=±2516=±54

x \: \in \: (0, \frac{\pi}{2} ) = > cosx > 0 = > cosx = \frac{4}{5}x∈(0,2π)=>cosx>0=>cosx=54

tgx = \frac{sinx}{cosx} = \frac{ \frac{3}{5} }{ \frac{4}{5} } = \frac{3}{4}tgx=cosxsinx=5453=43

ctgx = \frac{cosx}{sinx} = \frac{ \frac{4}{5} }{ \frac{3}{5} } = \frac{4}{3}ctgx=sinxcosx=5354=34

sau \: ctgx = \frac{1}{tgx} = \frac{1}{ \frac{3}{4} } = \frac{4}{3}sauctgx=tgx1=431=34