In class on Wednesday I completed a special triangle activity. The activity was based on the three types of special triangles that are found in math. Those three triangles are a thirty, sixty, and ninety degree triangle and the other one is a forty five, forty five, ninety degree triangle, the third ons is a varitation of the thirty sixty ninety triangle.
The thirty degree triangle is the one that matches up with the ordered pair of radical three over two and one half. It has a radian measure of pi over six.
The forty five degree triangle is the one that matches up with radical two over two and radical two over two. It has a radian measure of pi over four.
The sixty degree trianlge is the one that matches up with the ordered pair of one half and radical three over two.
This activity helps with the unit circle because these three triangles are what make up the unit circle. Once you find these three triangles you can find the other three quadrants of the circle. Simply add and simplify all the way around the circle.The triangle always has to be in the first quadrant. If you were to draw these triangles in any of the other quadrants the values of the degrees would go up, the radians would also increase, and lastly the ordered pairs would differ from positive and negative.
As you can see the radians change and the degrees go up according the the revolution of the circle, zero to three sixty. The thirty degree triangle is now at one hundred and fifty degrees with a radian measure of five pi over six, this being in the second quadrant. The forty five triangle is now at two hundred and twenty five degrees and has a radian measure of five pi over four, this being in the third quadrant. The sixty degree triangle is now at three hundred degrees and now has a radian measure of five pi over three, this being the fourth quadrant. Another thing to notice is how the ordered pairs transition from positive to negative according to the quadrant of the unit circle.
The coolest thing I learned from this activity was how by finding one part of the circle one can easily solve for the entire unit circle.
This activity will help me in this unit because I will be able to solve for the rest of the unit with ease or if not at least have a tool to refer to in case I get stuck with my work.
Something I never realized before about special right triangles and the unit circle is, this whole concept is new to me so its all pretty intresting.
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