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#