MATH2412 Precalculus/Trigonometry Practice Practice Flashcards

Comprehensive vocabulary flashcards covering concepts from MATH2412 Practice Tests 1, 2, 3, and the Final Exam, including trigonometry, vectors, polar coordinates, and conic sections.

Coterminal Angle

Angles that share the same terminal side; for example, finding an angle between $0^ ext{o}$ and $360^ ext{o}$ or $0$ and $2 ext{ extpi}$ radians that ends in the same position.

Sector Area

The area of a portion of a circle, calculated using a radius and a central angle (e.g., radius of $18 ext{ hinspace in}$ and central angle of $71^ ext{o}$).

Arc Length

The distance along the curved line of a circle subtended by a central angle.

Reference Angle

The acute angle formed by the terminal side of an angle and the horizontal axis, used to find exact values of trigonometric functions without a calculator.

Angle of Elevation

The angle measured upward from the horizontal to a point of interest, such as the top of a building seen from the ground.

Angle of Depression

The angle measured downward from the horizontal line of sight to an object, such as looking from the top of a lighthouse down to a ship.

Amplitude

The measure of the maximum displacement of a periodic function from its midline; represented as $A$ in the form $y = A ext{sin}(Bx) + D$.

Period

The horizontal length of one complete cycle of a periodic function.

Phase Shift

The horizontal translation of a trigonometric function, indicating how far the graph is shifted to the left or right.

Midline

The horizontal line halfway between the maximum and minimum values of a periodic function, represented by the equation $y = D$.

Restricted Domain

The specific interval of input values for functions like $y = ext{sin} ext{ exttheta}$, $y = ext{cos} ext{ exttheta}$, and $y = ext{tan} ext{ exttheta}$ that allows for the existence of inverse functions.

Trigonometric Identity

An equation involving trigonometric functions that is true for all values within its domain, such as $( ext{sin} ext{ hinspace}x - ext{cos} ext{ hinspace}x )^2 = 1 - ext{sin}(2x)$, which must be verified through algebraic manipulation.

General Solution

A solution to a trigonometric equation that accounts for all possible coterminal angles over an infinite domain, typically including a term like $2 ext{ extpi}k$ or $180^ ext{o}n$.

Law of Sines

A rule used to solve triangles (particularly when two angles and a side or two sides and an non-included angle are known) stating the ratio of sides to the sine of opposite angles is constant.

Law of Cosines

A rule used to solve triangles when two sides and the included angle ($SAS$) or three sides ($SSS$) are known.

Magnitude

The length of a vector, denoted as oldsymbol{ ext{ extbardbl} v ext{ extbardbl}}, which can be calculated for a position vector from point $P$ to point $Q$.

Unit Vector

A vector denoted as oldsymbol{u} that has a magnitude of $1$ and points in the same direction as a given vector oldsymbol{v}.

Polar Coordinates

A system for locating points in a plane using a distance from the origin ($r$) and an angle ($ext{ exttheta}$) from the positive x-axis, expressed as $(r, ext{ exttheta})$.

Ellipse

A conic section defined by an equation such as $3x^2 + 6y^2 = 18$, characterized by a center, vertices, foci, co-vertices, and a major axis.

Hyperbola

A conic section formed by the intersection of a plane with a double cone, defined by two separate curves that approach oblique asymptotes.

Latus Rectum

A line segment passing through the focus of a parabola, perpendicular to its axis of symmetry, with endpoints on the parabola itself.

Directrix

A fixed line used in the definition of a parabola; the distance from any point on the parabola to the focus is equal to its distance to this line.