Trigonometry Cheat Sheet

A quick shorthand table to remember which trig functions to use for given problems. Note that you really want to learn how to do this by reorganizing the trigonometric definitions themselves, but this serves as a quick reminder.

Note that I use the format atan(), asin(), acos() for the inverse trigonometric functions for three reasons:

• atan() is clearly visibly different from tan(), while the -1 in tan^-1() is often overlooked by students.

• Excel and nearly every programming language uses the atan(), etc. formats.

• The tan^-1() formats screw up the format for negative powers with inverse operations. This is especially true once you start working with powers of trig. such as sin²(x), sin³(x). It's an abomination I tell yah.

How to use the table:

Find the subheading that has the three properties you are trying to work with, two that you know, and one that you're trying to find out.

Then find the row with the property that you want in bold (blue background), and use the equation in that cell.

Angle (θ)	ADJ	OPP	HYP
Angle, adjacent and opposite
atan(opp/adj)	adj	opp
θ	opp x tan(θ)	opp
θ	adj	adj / tan(θ)
Angle, adjacent and hypotenuse
acos(adj/hyp)	adj		hyp
θ	hyp x cos(θ)		hyp
θ	adj		adj / cos(θ)
Angle, opposite and hypotenuse
asin(opp/hyp)		opp	hyp
θ		hyp x sin(θ)	hyp
θ		opp	opp / sin(θ)
Adjacent, opposite and hypotenuse (no angle).
	adj	opp	√(opp2+adj2)
	√(hyp2 – opp2)	opp	hyp
	adj	√(hyp2 – adj2)	hyp

E.g. if you had the adjacent and the opposite, and you wanted the angle, you would use the first subheading. 

In that subheading, the first row has the angle cell bolded, so the formula inside  is the one that you'd want to use.  

θ = atan(opp/adj)