How do you find the values of all six trigonometric functions of a right triangle ABC where C is the right angle, given a=1, b=3?

1 Answer
May 7, 2018

sin=(3sqrt10)/10
csc=sqrt10/3
cos=sqrt10/10
sec=sqrt10/1
tan=3
cot=1/3
Note: This is based on my interpretation of the diagram. Without more information it is impossible to know which side, a or b, is adjacent or opposite.

Explanation:

First, finish solving the reference triangle, using the Pythagorean Theorem:
a^2+b^2=c^2 Input knowns:
(1)^2+(3)^2=c^2 Simplify:
1+9=c^2 Isolate c:
c=sqrt10 Since c is the hypotenuse of a reference triangle it must be positive.

Using the definitions of trig functions (assuming a is "adjacent" and b is "opposite"):
sin=o/h=b/c=3/sqrt10=(3sqrt10)/10
csc=h/o=c/b=sqrt10/3
cos=a/h=a/c=1/sqrt10=sqrt10/10
sec=h/a=c/a=sqrt10/1
tan=o/a=b/a=3/1=3
cot=a/o=a/b=1/3
Note: This is based on my interpretation of the diagram. Without more information it is impossible to know which side, a or b, is adjacent or opposite.