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=9, b=40, c=41?

Answer 1

#{: (sin(A)=9/41,color(white)("XXX"),csc(A)=9/41), (cos(A)=40/41,,sec(A)=41/40), (tan(A)=9/40,,cot(A)=40/9) :}#

Explanation:

Given the triangle:

The 6 trigonometric values for `/_A` follow from the definition of the trigonometric functions.
e.g. `sin="opposite"/"hypotenuse"`

If you wanted the 6 trigonometric values for `/_B`
you could rotate the triangle and use the basic definitions.