How do you find the values of all six trigonometric functions of a right triangle ABC where C is the right angle, given b=7, c=8?

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Answer 1 · 2016-11-24T15:12:38

$sinA=0.484$ , $cosA=0.875$ , $tanA=0.5533$ , $cotA=1.807$ , $secA=1.143$ , $cscA=2.066$

and $sinB=0.875$ , $cosB=0.484$ , $tanB=1.807$ , $cotB=0.5533$ , $secB=2.066$ , $cscB=1.143$

As triangle $DeltaABC$ is right angled at $C$ and $b=7$ and hypotenuse $c=8$ ,

using Pythagoras theorem, the third side is $a=sqrt(8^2-7^2)=sqrt(64-49)=sqrt15=3.873$

We already know $/_C=90^o$ ,

as $sinB=sqrt15/8=0.4841$ $/_B=28.96^o$ and

$/_A=90^o-28.96^o=61.04^o$

Now $sinA=3.873/8=0.484$ , $cosA=7/8=0.875$ , $tanA=3.873/7=0.5533$ , $cotA=1/tanA=1/0.5533=1.807$ , $secA=8/7=1.143$ , $cscA=8/3.873=2.066$

and $sinB=0.875$ , $cosB=0.484$ , $tanB=1.807$ , $cotB=0.5533$ , $secB=2.066$ , $cscB=1.143$