Precalculus

# Key Terms

PrecalculusKey Terms

### Key Terms

damped harmonic motion
oscillating motion that resembles periodic motion and simple harmonic motion, except that the graph is affected by a damping factor, an energy dissipating influence on the motion, such as friction
double-angle formulas
identities derived from the sum formulas for sine, cosine, and tangent in which the angles are equal
even-odd identities
set of equations involving trigonometric functions such that if $f( −x )=−f( x ), f( −x )=−f( x ),$ the identity is odd, and if $f( −x )=f( x ), f( −x )=f( x ),$ the identity is even
half-angle formulas
identities derived from the reduction formulas and used to determine half-angle values of trigonometric functions
product-to-sum formula
a trigonometric identity that allows the writing of a product of trigonometric functions as a sum or difference of trigonometric functions
Pythagorean identities
set of equations involving trigonometric functions based on the right triangle properties
quotient identities
pair of identities based on the fact that tangent is the ratio of sine and cosine, and cotangent is the ratio of cosine and sine
reciprocal identities
set of equations involving the reciprocals of basic trigonometric definitions
reduction formulas
identities derived from the double-angle formulas and used to reduce the power of a trigonometric function
simple harmonic motion
a repetitive motion that can be modeled by periodic sinusoidal oscillation
sum-to-product formula
a trigonometric identity that allows, by using substitution, the writing of a sum of trigonometric functions as a product of trigonometric functions
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