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Questions and Answers
What theorem relates the lengths of the sides in a right triangle?
What theorem relates the lengths of the sides in a right triangle?
Which trigonometric function represents the ratio of the opposite side to the hypotenuse in a right triangle?
Which trigonometric function represents the ratio of the opposite side to the hypotenuse in a right triangle?
If the angle A in a right triangle is 30 degrees, what is tan(A)?
If the angle A in a right triangle is 30 degrees, what is tan(A)?
What is the reciprocal function of the cosine function?
What is the reciprocal function of the cosine function?
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Which trigonometric function is used to find the ratio of the adjacent side to the hypotenuse in a right triangle?
Which trigonometric function is used to find the ratio of the adjacent side to the hypotenuse in a right triangle?
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If the angle B in a right triangle is 60 degrees, what is cot(B)?
If the angle B in a right triangle is 60 degrees, what is cot(B)?
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What fundamental experiments were performed by scientists in the 18th and 19th century?
What fundamental experiments were performed by scientists in the 18th and 19th century?
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Who were the scientists that studied the structure of substances and the atom, leading to the discovery of the laws of chemical combination?
Who were the scientists that studied the structure of substances and the atom, leading to the discovery of the laws of chemical combination?
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What is the significance of Dalton’s atomic theory in writing molecular formulae of compounds?
What is the significance of Dalton’s atomic theory in writing molecular formulae of compounds?
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What apparatus is recommended for verifying the laws of chemical combination?
What apparatus is recommended for verifying the laws of chemical combination?
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What chemicals are used in the activity involving calcium chloride and sodium sulphate solutions?
What chemicals are used in the activity involving calcium chloride and sodium sulphate solutions?
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What should be done after inserting the test tube with sodium sulphate solution into the conical flask?
What should be done after inserting the test tube with sodium sulphate solution into the conical flask?
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What is the purpose of weighing the conical flask before and after pouring the solution?
What is the purpose of weighing the conical flask before and after pouring the solution?
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What happens when 56 g of calcium oxide is mixed with 18 g of water?
What happens when 56 g of calcium oxide is mixed with 18 g of water?
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What inference can be drawn from observing the reaction between calcium oxide and water?
What inference can be drawn from observing the reaction between calcium oxide and water?
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How do the experiments with calcium chloride, sodium sulphate, calcium oxide, and water relate to the laws of chemical combination?
How do the experiments with calcium chloride, sodium sulphate, calcium oxide, and water relate to the laws of chemical combination?
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Study Notes
Trigonometry
Solving Triangles
To solve triangles, we use the Pythagorean Theorem. It states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of the other two sides. Mathematically: h² = l² + b².
Trigonometric Equations
Trigonometric equations are used to solve problems involving angles and their relationships with side lengths in triangles. There are six basic trigonometric functions: sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc). These functions relate the sides of a right triangle to one another, based on the angle being measured. For example, sin(A) is the ratio of the length of the side opposite an acute angle A to the hypotenuse. Similarly, cos(A) is the ratio of the length of the adjacent side to the hypotenuse. tan(A) is the ratio of the length of the side opposite to A over the length of the side adjacent to A, and so on.
Trigonometric Functions
The six fundamental trigonometric functions are used to calculate the values of other trigonometric functions for different angles. They are defined as follows:
- Sine: sin(θ) = opp / hyp
- Cosine: cos(θ) = adj / hyp
- Tangent: tan(θ) = opp / adj
- Cosecant: csc(θ) = 1 / sin(θ)
- Secant: sec(θ) = 1 / cos(θ)
- Cotangent: cot(θ) = 1 / tan(θ)
These functions have various applications in different fields such as astronomy, mapmaking, surveying, and artillery range finding.
Surface Area and Volume
Using trigonometry, we can find both surface area and volume of various shapes:
-
Surface Area of a Sphere: The formula for calculating the surface area of a sphere is
4πr^2, where r is the radius of the sphere. -
Volume of a Cylinder or Prism: The formula for calculating the volume of a cylinder or prism is
V = l * h, where l represents the base area and h represents the height of the cylinder or prism.
Circle Coordinate Geometry
In coordinate geometry, circles play an important role. The equation of a circle centered at (a, b) with radius r is given by (x - a)^2 + (y - b)^2 = r^2. This equation describes the relationship between points on the circle and their coordinates in a two-dimensional plane.
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Description
Learn about solving triangles using the Pythagorean Theorem, trigonometric equations, functions, surface area and volume calculations, and circle coordinate geometry. Understand how trigonometry is applied in various fields like astronomy, mapmaking, surveying, and more.
