Question

What is the value of `sin` in terms of `cos`, and of `cos` in terms of `sin`?

Answer 1

See below but the relation is based on the general formula `sin^2+cos^2=1` and application of the CAST rule for which basic trig functions are positive in which quadrants,

Explanation:

#{: ("In Quadrant I:", color(white)("xx"),sin = +sqrt(1-cos^2), color(white)("xx"),cos=+sqrt(1-sin^2)), ("In Quadrant II:", color(white)("xx"),sin = +sqrt(1-cos^2), color(white)("xx"),cos=-sqrt(1-sin^2)), ("In Quadrant III:", color(white)("xx"),sin = -sqrt(1-cos^2), color(white)("xx"),cos=-sqrt(1-sin^2)), ("In Quadrant IV:", color(white)("xx"),sin = -sqrt(1-cos^2), color(white)("xx"),cos=+sqrt(1-sin^2)) :}#