How do you find the values of all six trigonometric functions of a right triangle ABC where C is the right angle, given a=5, b=12, c=13?

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Answer 1 · 2017-07-19T20:26:48

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So let's start with the angle #hatA# :

#sin hatA=a/c=5/13#

#cos hatA=b/c=12/13#

#tan hatA=a/b=5/12#

#cot hatA=b/a=12/5#

#sec hatA=1/cos hatA=13/12#

#csc hatA=1/sin hatA=13/5#

Now for the angle #hatB# :

#sin hatB=B/c=12/13#

#cos hatB=a/c=5/13#

#tan hatB=b/a=12/5#

#cot hatB=a/b=5/12#

#sec hatB=1/cos hatB=13/5#

#csc hatB=1/sin hatB=13/12#