The unit circle
I can appreciate that the trigonometric functions are derived from measurements within a unit circle.
The unit circle
I can appreciate that the trigonometric functions are derived from measurements within a unit circle.
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Lesson details
Key learning points
- The unit circle is a circle with a radius of one.
- The unit circle is centered on the origin.
- The sine of an angle is the y-coordinate of the point where the radius has been rotated through that angle.
- The cosine of an angle is the x-coordinate of the point where the radius has been rotated through that angle.
- The tangent of an angle is the length of the side opposite the angle along the tangent at x = 1 to the unit circle.
Keywords
Trigonometric functions - Trigonometric functions are commonly defined as ratios of two sides of a right-angled triangle for a given angle.
Sine function - The sine of an angle (sin(θ°)) is the y-coordinate of point P on the triangle formed inside the unit circle.
Cosine function - The cosine of an angle (cos(θ°)) is the x-coordinate of point P on the triangle formed inside the unit circle.
Tangent function - The tangent of an angle (tan(θ°)) is the y-coordinate of point Q on the triangle which extends from the unit circle.
Common misconception
When reading the values of the trigonometric functions during the explanation slides and the tasks, pupils may think that all the values taken from the graphs are fully accurate.
Explain that many of the values from the trigonometric functions have digits beyond the second decimal place. However, two decimal places is a reasonable degree of accuracy for reading values from the graphs during this lesson.
To help you plan your year 9 maths lesson on: The unit circle, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 9 maths lesson on: The unit circle, download all teaching resources for free and adapt to suit your pupils' needs.
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Explore more key stage 3 maths lessons from the Trigonometry unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
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Lesson video
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Starter quiz
6 Questions
