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?

1 Answer
Jul 19, 2017

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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