Which function do I need to use to calculate the opposite side of a triangle when the angle is known and the hypotenuse?

sin(1.2°) = opposite/hypotenuse

Old Mnemonic “soak a toe”

SOH CAH TOA

sine = opposite/hypotenuse

cosine = adjacent/hypotenuse

tangent = opposite/adjacent

A modern formulation is in terms of coordinates on the unit circle where x^2+y^2 = 1

a point (x,y) has a ray from (0,0) going through it which makes an angle theta measured counter clockwise from the postive x axis. Thus (x,y) = (cos(theta),sin(theta)). Many identities including sin^2(t) + cos^2(t) = 1 are easily seen or derived. For example: signs of functions in Q1 to Q4, negative angles, complementary and supplementary angles. Also special values in degrees or radians.

If you define sine and cosine in terms of complex exponentials based on Euler’s identity, then addition, subtraction, double angle, half angle identities are almost immediate without referring to geometry at all.