Question

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, c=6?

Answer 1

(see below)

Explanation:

Based on the Pythagorean Theorem, we know that
#color(white)("XXX")a^2+b^2=c^2

`rarr b=sqrt(c^2-a^2)=sqrt(6^2-5^2)=sqrt(11)`

`sin = "opposite"/"hypotenuse"color(white)("XX")rarr sin(A)=5/6`

`csc = "hypotenuse"/"opposite" color(white)("XX")rarr csc(A)=6/5`

`cos = "adjacent"/"hypotenuse"color(white)("XX")rarr cos(A)=sqrt(11)/6`

`sec = "hypotenuse"/"adjacent" color(white)("XX")rarr sec(A)=6/sqrt(11)`

`tan = "opposite"/"adjacent"color(white)("XX")rarr tan(A)=5/sqrt(11)`

`cot = "adjacent"/"opposite" color(white)("XX")rarr cot(A)=sqrt(11)/5`