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Age 16 to 18 Short
Challenge Level
In this diagram OA is a radius of a unit circle. The hypotenuse of the large triangle is tangent to the circle at A.Find the lengths $\cos(a)$, $\sin(a)$, $\tan(a)$, $\frac{1}{\cos(a)}$, $\frac{1}{\sin(a)}$ and $\frac{1}{\tan(a)}$ in the diagram.
Find the areas of all of the regions in the diagram.
Did you know ... ?
Whilst trigonometric functions are defined algebraically in more advanced applications, geometric images such as this one can give great insight into the relationships between the functions. They also impart a sense of the beauty and interconnectedness of mathematics, which inspires many students of mathematics.
Whilst trigonometric functions are defined algebraically in more advanced applications, geometric images such as this one can give great insight into the relationships between the functions. They also impart a sense of the beauty and interconnectedness of mathematics, which inspires many students of mathematics.
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.