### Geometrical look at tangens

As mathematics is an important part of my life (I'm a teacher educator in mathematics), I thought it would be a good idea to start a blog where interesting small mathematical details could be posted...

Just a few weeks ago, I had a little revelation in trigonometry. I've been teaching trigonometry for years, and have given the definition of sin, cos and tan according to the triangle and the unit circle. I have never seen tangens clearly in the unit circle however - not before I came across this application. While cos u is the x-coordinate of the intersection of the one leg of the angle and the circle, and sin u is the y-coordinate of the same intersection, I have never before seen that tan u is the intersection of the leg and the vertical line x=1. A nice fact...

(And yes, I know I should have an illustration here, but for now the link to the Java-thing will do...)

Just a few weeks ago, I had a little revelation in trigonometry. I've been teaching trigonometry for years, and have given the definition of sin, cos and tan according to the triangle and the unit circle. I have never seen tangens clearly in the unit circle however - not before I came across this application. While cos u is the x-coordinate of the intersection of the one leg of the angle and the circle, and sin u is the y-coordinate of the same intersection, I have never before seen that tan u is the intersection of the leg and the vertical line x=1. A nice fact...

(And yes, I know I should have an illustration here, but for now the link to the Java-thing will do...)

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