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Questions and Answers
What is the definition of the sine of an angle in a right-angled triangle?
What is the Pythagorean Identity in trigonometry?
What is the period of the sine and cosine graphs?
What is the application of trigonometry in the study of curves and shapes?
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What is the definition of the tangent of an angle in a right-angled triangle?
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What is the formula for sin(A + B)?
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What is the application of trigonometry in modeling periodic phenomena?
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What is the definition of the cosecant of an angle in a right-angled triangle?
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Study Notes
Trigonometry
Definition
- Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles.
Key Concepts
- Angles: Measured in degrees, radians, or gradients.
- Triangles: Right-angled triangles are a fundamental concept in trigonometry.
- Trigonometric Ratios: Relationships between the sides and angles of triangles.
Trigonometric Ratios
- Sine (sin): Opposite side / Hypotenuse
- Cosine (cos): Adjacent side / Hypotenuse
- Tangent (tan): Opposite side / Adjacent side
- Cotangent (cot): Adjacent side / Opposite side
- Secant (sec): Hypotenuse / Adjacent side
- Cosecant (csc): Hypotenuse / Opposite side
Identities
- Pythagorean Identity: sin^2(A) + cos^2(A) = 1
-
Sum and Difference Formulas:
- sin(A + B) = sin(A)cos(B) + cos(A)sin(B)
- cos(A + B) = cos(A)cos(B) - sin(A)sin(B)
Graphs
- Sine and Cosine Graphs: Periodic waves with amplitude 1 and period 2Ï€.
- Tangent Graph: Periodic wave with asymptotes at π/2 and -π/2.
Applications
- Right Triangle Problems: Solving problems involving right-angled triangles.
- Wave Motion: Modeling periodic phenomena, such as sound and light waves.
- Analytic Geometry: Trigonometry is used in the study of curves and shapes.
Trigonometry
Definition and Basics
- Trigonometry studies relationships between triangle sides and angles.
- Angles can be measured in degrees, radians, or gradients.
- Right-angled triangles are fundamental in trigonometry.
Trigonometric Ratios
- Sine (sin) = Opposite side / Hypotenuse
- Cosine (cos) = Adjacent side / Hypotenuse
- Tangent (tan) = Opposite side / Adjacent side
- Cotangent (cot) = Adjacent side / Opposite side
- Secant (sec) = Hypotenuse / Adjacent side
- Cosecant (csc) = Hypotenuse / Opposite side
Trigonometric Identities
- Pythagorean Identity: sin^2(A) + cos^2(A) = 1
- Sum and Difference Formulas:
- sin(A + B) = sin(A)cos(B) + cos(A)sin(B)
- cos(A + B) = cos(A)cos(B) - sin(A)sin(B)
Graphs
- Sine and cosine graphs: periodic waves with amplitude 1 and period 2Ï€.
- Tangent graph: periodic wave with asymptotes at π/2 and -π/2.
Real-World Applications
- Solving right triangle problems.
- Modeling periodic phenomena: sound and light waves.
- Analytic geometry: studying curves and shapes.
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Description
Learn the fundamental concepts of trigonometry, including angles, triangles, and trigonometric ratios such as sine and cosine. Understand the relationships between the sides and angles of triangles.
