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Questions and Answers
What is the intersection of two planes in geometry?
What is the intersection of two planes in geometry?
What is the sum of the interior angles of a quadrilateral?
What is the sum of the interior angles of a quadrilateral?
What is the value of sin(A) if A is 30°?
What is the value of sin(A) if A is 30°?
What is the cosine rule used for?
What is the cosine rule used for?
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What is the relationship between the angles in the same segment of a circle?
What is the relationship between the angles in the same segment of a circle?
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What is the Pythagorean identity?
What is the Pythagorean identity?
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What is the primary difference between contact forces and non-contact forces?
What is the primary difference between contact forces and non-contact forces?
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Which of Newton's laws states that an object at rest will remain at rest unless acted upon by an external force?
Which of Newton's laws states that an object at rest will remain at rest unless acted upon by an external force?
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What is the formula for kinetic energy?
What is the formula for kinetic energy?
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What is the purpose of a force diagram?
What is the purpose of a force diagram?
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Which type of energy is associated with the motion of charged particles?
Which type of energy is associated with the motion of charged particles?
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What is the formula for potential energy?
What is the formula for potential energy?
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Study Notes
Geometry
Points, Lines, and Planes
- A point has no size, only location
- A line extends infinitely in two directions
- A plane is a flat surface that extends infinitely in all directions
- Intersection of two lines: one point
- Intersection of two planes: a line
- Intersection of three planes: a point
Angles
- Acute angle: less than 90°
- Right angle: exactly 90°
- Obtuse angle: greater than 90°
- Straight angle: exactly 180°
- Reflex angle: greater than 180°
- Complementary angles: add up to 90°
- Supplementary angles: add up to 180°
Properties of Shapes
- Congruent shapes: same size and shape
- Similar shapes: same shape, different size
- Interior angle sum of a triangle: 180°
- Interior angle sum of a quadrilateral: 360°
- Exterior angle of a polygon: equal to the sum of the interior angles
Circle Theorems
- Angle at the center: twice the angle at the circumference
- Angles in the same segment: equal
- Cyclic quadrilateral: opposite angles add up to 180°
- Tangent and radius: perpendicular
- Tangents from the same point: equal in length
Trigonometry
Right-Angled Triangles
- Sine (sin): opposite side / hypotenuse
- Cosine (cos): adjacent side / hypotenuse
- Tangent (tan): opposite side / adjacent side
- Pythagorean identity: sin^2 + cos^2 = 1
- Trigonometric ratios: sin, cos, and tan of common angles (30°, 45°, 60°)
Graphs of Trigonometric Functions
- Sine graph: periodic, wave-like, amplitude 1
- Cosine graph: periodic, wave-like, amplitude 1
- Tangent graph: periodic, wave-like, asymptotes at 90° and 270°
Solving Triangles
- Angle-sum identity: sin(A)/a = sin(B)/b = sin(C)/c
- Sine rule: a/sin(A) = b/sin(B) = c/sin(C)
- Cosine rule: a^2 = b^2 + c^2 - 2bc cos(A)
- Area of a triangle: (1/2)ab sin(C)
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Description
Learn about points, lines, planes, angles, properties of shapes, circle theorems, and trigonometry concepts, including right-angled triangles, trigonometric functions, and solving triangles.
