How the Trigonometry Functions Are Related

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The relationships between the six major trigonometric functions (sine, cosine, tangent, secant, cosecant, and cotangent) can all be seen on a single right-angled triangle inside a circle. As you drag the red point around the edge of the circle, you can see how the six functions increase or decrease in value. Only sine and cosine stay inside the circle; at some angles, the others escape to infinity.


Mouseover the function name to see its current value.


Contributed by: C. Ormullion (August 2013)
Open content licensed under CC BY-NC-SA



The three less well-known functions in the family (cotangent, cosecant, secant) are the reciprocals of their better-known siblings: , , . The diagram clearly shows why cotangent becomes very large as the tangent gets smaller, and why sine and its reciprocal cosecant are both 1 when the red point reaches the top of the circle. The secant goes to infinity as cosine gets close to 0.

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