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trig functions graphs
A LevelMathematics~5 min read
Overview
This lesson introduces the fundamental trigonometric functions (sine, cosine, tangent) and explores their graphical representations. We will analyse their key properties, including periodicity, amplitude, and asymptotes, and understand how transformations affect these graphs.
Introduction to Sine, Cosine, and Tangent Functions
The **sine (sin x)**, **cosine (cos x)**, and **tangent (tan x)** functions are fundamental to trigonometry. They are defined using the unit circle, a circle with a radius of 1 unit centered at the origin (0,0). * **sin x**: For an angle x (measured counter-clockwise from the positive x-axis), si...
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Key Concepts
- Sine Function (sin x): A periodic function representing the y-coordinate of a point on the unit circle corresponding to an angle x.
- Cosine Function (cos x): A periodic function representing the x-coordinate of a point on the unit circle corresponding to an angle x.
- Tangent Function (tan x): A periodic function defined as sin x / cos x, representing the slope of the line from the origin to a point on the unit circle.
- Periodicity: The property of a function where its values repeat at regular intervals.
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Exam Tips
- →Always state the period and amplitude (if applicable) when sketching trigonometric graphs. Clearly label axes and key points like intercepts and turning points.
- →For tangent graphs, explicitly draw and label the equations of the vertical asymptotes. These are critical features and often carry marks.
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