Unit 3 - Trigonometric Functions

Periodic Function

A function with values that repeat at regular intervals. There exists a positive real number c such that f(t+c)=f(t) for all values of t in the domain of f.

Damped wave

A wave whose amplitude decreases, such as the graph of a damped trigonometric function.

co-terminal angles

Angles in standard position that have the same initial and terminal sides, but different measures

Law of Sines

Establishes a relationship between the angles and the side lengths of ΔABC: a/sin(A) = b/sin(B) = c/sin(C).

Frequency

For a sinusodial function, the number of cycles the function completes in a one unit interval. The frequency is the reciprocal of the period. For y=asin(bx+c)+d and y=acos(bx+c)+d, frequency = 1/period or |b|/2pi

Vertical shift

For a sinusoidal function, a vertical translation that is the average of the maximum and minimum values of the function.

Sector

In a circle, the region bounded by a central angle and it's intercepted arc

Damping Factor

In a damped trigonometric function of the form y=f(x) sinbx or y=f(x) cosbx, f(x) is the damping factor

Terminal Side

The final position of a ray after rotation when forming an angle

damped trigonometric function

The function formed when a sinusoidal function (y=sinbx) or (y=cosbx) is multiplied by another function (y=f(x)). A function of the form y=f(x) sinbx or y=f(x) cosbx

Linear Speed

The rate at which an object moves along a circular path

initial side

The starting position of a ray when forming an angle

Unit Circle

a circle with a radius of 1, centered at the origin of a coordinate system

Sine Curve

a curve representing periodic oscillations of constant amplitude as given by a sine function.

Trigonometric Function

a function of an angle, or of an abstract quantity, used in trigonometry, including the sine, cosine, tangent, cotangent, secant, and cosecant, and their hyperbolic counterparts.

Radian

a unit of angular measurement equal to 180/π or 57.269°

quadrantal angle

an angle in standard position that has a terminal side that lies on one of the coordinate axes

standard position

an angle positioned so that is at the origin and it's initial side is along the positive x-axis

Sinusoid

any transformation of a sine function

Law of Cosines

a²=b²+c²-2bcCosA, b²=a²+c²-2acCosB, c²=a²+b²-2abCosC, is used to find the remaining parts of an oblique (non-right) triangle when either the lengths of two sides and the measure of the included angle is known (SAS) or the lengths of the three sides (SSS) are known

Period

for a function y=f(t), the smallest positive number c for which f(t+c) = f(t)

Phase Shift

for a sinusoidal function, the difference between the horizontal position of a function and that of an otherwise similar sinusoidal function

Amplitude

half the distance between the max and min values of a sinusoidal function for y = a sin (bx + c) + d, amplitude = |a|

Inverse Trigonometric Functions

sin−1(x) , cos−1(x) , and tan−1(x) , are used to find the unknown measure of an angle of a right triangle when two side lengths are known.

Reference Angle

the acute angle formed by the terminal side of an angle in standard position and the x-axis

Angle of Elevation

the angle formed by a horizontal line and an observer's line of sight to an object above

Angle of Depression

the angle formed by a horizontal line and an observer's line of sight to an object below

angular speed

the rate at which the object rotates about a fixed point

Damped Oscillation

the reduction in amplitude of a sinusoidal wave of a damped trigonometric function