How do you find the 6 trigonometric functions for 0 degrees?

1 Answer
Alan P.
Aug 18, 2015

sin(0^o) = 0color(white)("XXXX")csc(0^o) "undefined"
cos(0^o)=1color(white)("XXXX")sec(0^o)=1
tan(0^o)=0color(white)("XXXX")cot(0^o) "undefined"

Explanation:

Using a triangle in standard position with the angle involved at the origin,
the 6 basic trigonometric functions are defined as

sin = "opposite"/"hypotenuse"color(white)("XXXX")csc ="hypotenuse"/"opposite"

cos = "adjacent"/"hypotenuse"color(white)("XXXX")sec ="hypotenuse"/"adjacent"

tan = "opposite"/"adjacent"color(white)("XXXX")cot="adjacent"/"opposite"

enter image source here

From the above image we can see that as the angle approaches 0

  • the length of the opposite side also approaches 0 and

  • the length of the hypotenuse and the length of the adjacent side become equal.

This gives the values as in the "Answer" for the 6 basic trig functions.

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