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Questions and Answers
What does the sine function represent?
Which trigonometric function is denoted by 'cos'?
What does the tangent function measure?
Which trigonometric function refers to the ratio of the adjacent side over the hypotenuse?
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What do trigonometric functions help determine in finance and economics?
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Apart from geometry and physics, in which other fields are trigonometric functions applied?
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What is the period of all trigonometric functions?
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If sin(x) = y, what is sin(-x) equal to?
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What is the value of cos($A + B$) using the sum formula?
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What is the sum formula for tan($A + B$)?
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What happens to the output of a trigonometric function if we add a full circle (360 degrees) to the angle?
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If cos(x) = z, what is cos(-x) equal to?
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Study Notes
Maths Class 11 Chapter 3: Trigonometric Functions
Trigonometry is a branch of mathematics dealing with the relationships between the angles of triangles and the ratios of their sides. In your maths class 11, you'll likely study trigonometric functions as part of the broader scope of geometry and algebra. Here's what you can expect when it comes to understanding these functions within the context of Chapter 3.
Basic Concepts
Trigonometric functions are used to relate angles to the ratios of lengths of the sides of right-angled triangles. They include sine, cosine, and tangent.
Sine Function
The sine function refers to the ratio of the side opposite an angle to the longest side of the triangle, typically referred to as the hypotenuse. It is denoted by sin.
Cosine Function
Cosine is the ratio of the adjacent side over the hypotenuse. It is represented by cos.
Tangent Function
Tangent measures the ratio of the length of the side opposite the angle divided by the length of the adjacent side.
These functions play crucial roles in various mathematical applications, such as in geometry, physics, engineering, and even in finance and economics where they determine interest rates, profit margins, cost of capital, etc.
Properties of Trigonometric Functions
While studying these functions, you will also learn about properties like periodicity, symmetry, identity, and sum/difference formulas. These properties help simplify calculations and find relationships among different angles and their respective trigonometric values. Some key properties include:
Periodicity
All trigonometric functions have a period of 2Ï€. This means that if we add 2Ï€ radians or 360 degrees (one full circle) to the angle of any trigonometric function, the output remains unchanged. For example, if tan(x)=y, then tan(x+2Ï€)=tan(x).
Symmetry
Trigonometric functions have certain symmetries which allow us to easily find their value at an angle other than those given. For instance, sin(-θ) = -sin(θ), cos(-θ) = cos(θ), and tan(-θ) = -tan(θ).
Sum and Difference Formulas
These formulas enable researchers to calculate trigonometric values of sums and differences of two angles without needing to compute them separately. Examples include:
- sin(A + B) = sin(A)cos(B) + cos(A)sin(B)
- cos(A + B) = cos(A)cos(B) - sin(A)sin(B)
- tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))
By mastering these concepts and properties, students can solve complex problems involving trigonometry effectively.
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Description
Learn about trigonometric functions in your Maths Class 11 Chapter 3. Understand the basic concepts of sine, cosine, and tangent functions, along with the properties like periodicity, symmetry, and sum/difference formulas. These concepts are crucial for various mathematical applications in geometry, physics, engineering, finance, and economics.
