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Trigonometry

Trigonometry is useful in determining linear lengths / oscillation with respect to digital art.

Artists traditionally use angles to measure rotations:

an angle

an angle θ

right angle

right angle

complementary angle

The complementary angles a and b (b is the complement of a, and a is the complement of b)

various angles

Acute (a), obtuse (b), and straight (c) angles. Here, a and b are supplementary angles

Given a triangle, trigonometry can be used to determine angles and side lengths if some information is known:

triangle reference

reference triangle with marked angles, sides and terms

sine

sine function

cosine

cosine function

tangent

tangent function

these can be memorized using the mnemonic soh-cah-toa

We can make use of radians and advanced trig functions as well:

radian graphical representation

graphical representation of a radian

radian formula

formula to convert radians to degrees. radians should be converted to degrees once calculations are done because degrees are more familiar to us

radian plot

radian plot in common degree increments

advanced trigonometry

introduction of secant, cosecant, and cotangent

Given these formulas we can solve for the variables:

tangent calculation

calculation of a tangent angle using the formula and converting from radians

Oscillation can be represented with sine and cosine curves once plotted:

sine and cosine curve plot

sine and cosine curve