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 sin^{2}(x), sin^{3}(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

√(opp^{2}+adj^{2})


√(hyp^{2}
– opp^{2})

opp

hyp


adj

√(hyp^{2}
– adj^{2})

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)
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