MTH 162 PreCalculus Unit 4: Applications of Trigonometry and Analytic Geometry

These flashcards cover key concepts and formulas related to the applications of trigonometry and analytic geometry, including the Law of Sines, Law of Cosines, area calculations, and properties of conic sections.

Law of Sines

In a triangle with sides a, b, and c opposite angles A, B, and C, the Law of Sines states that \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}.

Law of Cosines

In a triangle with sides a, b, and c opposite angles A, B, and C, the Law of Cosines states that c^2 = a^2 + b^2 - 2ab \cos C, and similar formulas for the other sides.

Triangle Area

The area of a triangle can be calculated as \text{Area} = \frac{1}{2}ab \sin \gamma or using Heron's formula: \text{Area} = \sqrt{s(s-a)(s-b)(s-c)} where s is the semi-perimeter.

Semi-perimeter

The semi-perimeter of a triangle is calculated by the formula s = \frac{a + b + c}{2}.

Parabola

A parabola is defined by the equation y = \frac{1}{4p}x^2, where one variable is squared.

Ellipse

An ellipse is defined by the equation \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1, representing a conic section.

Hyperbola

A hyperbola is defined by the equation \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1, representing a conic section.

Focus of a Parabola

For a parabola represented by y = \frac{1}{4p}x^2, the focus is at the point (0, p).

Major Axis of an Ellipse

The major axis of an ellipse defined by \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 is aligned along the x-axis with endpoints (±a, 0).

Asymptotes of a Hyperbola

The asymptotes of a hyperbola represented by \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 are given by the equations y = \pm \frac{b}{a} x.