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Questions and Answers
What is the geometric mean?
What is a Pythagorean triple?
A set of three nonzero whole numbers a, b, and c, such that a^2 + b^2 = c^2.
What does cosine represent in right triangle trigonometry?
Adj/hyp
What does sine represent in right triangle trigonometry?
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What does tangent represent in right triangle trigonometry?
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What is a trigonometric ratio?
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What does the term 'trigonometry' mean?
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What is the inverse cosine?
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What is the inverse sine?
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What is the inverse tangent?
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What is the angle of elevation?
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What is the angle of depression?
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What is the Law of Sines used for?
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What is the Law of Cosines used for?
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What does magnitude refer to in vector terms?
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How is direction expressed in vector analysis?
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What defines a vector?
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What is a resultant vector?
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What is meant by standard position in terms of vectors?
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What is component form of a vector?
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Study Notes
Geometry Chapter 8 Vocabulary

Geometric Mean: The positive square root of the product of two numbers, often used in proportions and averages.

Pythagorean Triple: A set of three positive integers ( a, b, c ) that satisfy the condition ( a^2 + b^2 = c^2 ), forming a right triangle.

Cosine: A trigonometric function defined as the ratio of the length of the adjacent side to the hypotenuse in a right triangle, represented as ( \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} ).

Sine: A trigonometric function defined as the ratio of the length of the opposite side to the hypotenuse, expressed as ( \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} ).

Tangent: A trigonometric function representing the ratio of the length of the opposite side to the adjacent side, written as ( \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} ).

Trigonometric Ratio: The ratio of the lengths of two sides of a right triangle, fundamental in trigonometric applications.

Trigonometry: Derived from "trigon" (triangle) and "metron" (measure), it is the mathematical study of relationships involving angles and side lengths in triangles.

Inverse Cosine: The function that determines the angle whose cosine is a given value, denoted as ( \cos^{1} ).

Inverse Sine: The function that determines the angle whose sine is a given value, denoted as ( \sin^{1} ).

Inverse Tangent: The function that determines the angle whose tangent is a given value, denoted as ( \tan^{1} ).

Angle of Elevation: The angle formed between a horizontal line and a line of sight extending upward from the horizontal.

Angle of Depression: The angle formed between a horizontal line and a line of sight extending downward from the horizontal.

Law of Sines: A mathematical rule used to find unknown side lengths and angle measures in any triangle, applicable with AngleAngleSide (AAS) or AngleSideAngle (ASA) configurations.

Law of Cosines: A formula used to solve triangles when two sides and the included angle (SideAngleSide, SAS) are known, providing relationships between side lengths and angles.

Magnitude: Refers to the length of a vector, measured as the distance from its initial point to its terminal point.

Direction: The orientation of a vector, represented by the angle it forms with the horizontal or the measurement in degrees (0° to 90°) east or west of the northsouth line.

Vector: A quantity described by both magnitude and direction, essential for representing variables in physics and mathematics.

Resultant: The single vector that results from the vector addition of two or more vectors, encapsulating their combined effect.

Standard Position: A term describing a vector when its initial point is located at the origin of a coordinate system.

Component Form: A way to express a vector using its initial point and final point, typically in the format (x, y), indicating its horizontal and vertical components.
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Test your knowledge of key terms in Geometry Chapter 8 with these flashcards. Each card highlights important concepts such as geometric mean, pythagorean triples, and trigonometric ratios. Perfect for students looking to enhance their understanding of geometry vocabulary.