Questions and Answers
What is the definition of trigonometry?
Which of the following is NOT a type of angle as classified in trigonometry?
What is the relationship among the angles in a triangle?
The Pythagorean Theorem is applicable in which type of triangle?
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In which scenario would you use Heron’s Formula?
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Which law would you use to solve for unknown sides of an oblique triangle when you know two sides and the angle opposite one of them?
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What defines a reflex angle?
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What does the symbol θ (theta) typically represent in trigonometry?
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What property distinguishes the sides of a spherical triangle from those of a plane triangle?
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What is the range of the sum of interior angles in a spherical triangle?
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Which formula is essential for calculating the area of a spherical triangle?
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Which of the following statements about right spherical triangles is true?
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What does the sine law in oblique spherical triangles relate to?
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What is the primary purpose of latitudes and longitudes on the terrestrial sphere?
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Which conversion represents 1° in nautical miles?
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What is the definition of the Prime Meridian in relation to longitudes?
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Study Notes
Trigonometry Overview
- Originates from Greek “trigonon" (triangle) and “metria" (measurement)
- Focuses on relationships of sides and angles in triangles
- Hipparchus known as the Father of Trigonometry
Angles
- Defined as the space between two intersecting lines
- Vertex is the point where the lines intersect
- Angle types:
- Zero (Null): θ = 0°
- Acute: 0 < θ < 90°
- Right: θ = 90°
- Obtuse: 90° < θ < 180°
- Straight: θ = 180°
- Reflex: 180° < θ
Right Triangle and Theorems
- Uses Pythagorean Theorem to relate the lengths of sides
- Triangle angle sum property: A + B + C = 180°
Trigonometric Functions and Identities
- Trigonometric Functions: sine, cosine, tangent, etc.
- Reciprocal Identities: cotangent, secant, cosecant
- Pythagorean Identities: relationships between sine, cosine, and tangent functions
- Sum & Difference and Double Angle Identities for angle manipulations
Laws for Oblique Triangles
- Sine Law: Relates the ratio of sides to the sine of opposite angles
- Cosine Law: Relates the lengths of sides to the cosine of one angle
Area of Triangle Calculations
- Area using base and height
- Area given two sides and included angle
- Heron’s Formula for area given all three sides
Circle Theorems
- Angles subtended by the same arc are equal
- Inscribed angle is half the measure of the central angle
- Various intersection theorems with chords, tangents, and secants
Quadrantal Trigonometric Functions
- Utilize acronym ACT for reference
- Outline S+ function relationships
Spherical Trigonometry
- Studies triangle measurements on spheres, crucial in navigation and astronomy
- Spherical triangles differ from plane triangles in measurement
- Interior angle sum varies:
- Plane: A + B + C = 180°
- Spherical: 180° < A + B + C < 540°
Formulas for Spherical Triangles
- Area and Volume formulas depend on spherical excess/defect
Types of Spherical Triangles
- Right Spherical Triangle: Has one right angle (90 degrees)
- Oblique Spherical Triangle: No right angles
Solutions for Spherical Triangles
- Right triangles utilize:
- Sin-Tan-Ad Rule: sine of middle part = product of tangents of adjacent parts
- Sin-Cos-Op Rule: sine of middle part = product of cosines of opposite parts
- Oblique triangles apply Sine and Cosine Laws with sign conventions for angles and sides
Terrestrial Sphere
- Assumes Earth as a perfect sphere for calculations
- Navigation units:
- 1 minute = 1 nautical mile (6080 feet)
- 1 statute mile = 5280 feet
- 1 knot = 1 nautical mile per hour
Geographic Coordinate System
- Latitudes: Circles parallel to the equator, indicating angular elevation
- Longitudes (meridians): Semicircles connecting poles, indicating east-west position
- Prime Meridian: Reference line running from north to south pole through Greenwich, England
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Description
Explore the fundamentals of Plane Trigonometry, including key concepts such as angles, triangles, and their measurements. This quiz will test your understanding of the relationships between the sides and angles of triangles, as well as essential trigonometric functions. Perfect for students looking to strengthen their math skills.
