Friday, February 21, 2014

I/D#1 Unit: N Concept 7 Unit Circle

The activity we did in class was a worksheet where we were given three different triangles of a 30 60 90 a 45 45  and a 60 30 90. We set the hypotenuse to one and solved for the opposing sides according to 30, 60, and 90. We then labeled what was r x and y for all three triangles. We then drew a coordinate plan so the triangle lies on t
he origin. We then labeled the three points of the triangle accordingly.











 

  Inquiry activity summary:
1.The 30 degree triangle consist of radical 3 over 2 as the x value and 1/2 as the y value when the hypotenuse is one. The reference angle is 30 degrees because its 30 degrees from the x axis.

2.The 45 degree triangle consist of equal value  sides in which has the value of radical 2 over 2 when the hypotenuse is one. The 45 degree angle has a 45 degree reference angle since its 45 degrees away from the x axis.

3. The 60 degree triangle has the x value of 1/2 and the y value is radical 3 over 2.  The 60 degree has a reference angle of 60 because its 60 degrees away from the x axis.

4. This activity helps me understand the unit circle in that the first quadrant consists of these angles and the whole circle is just full of these different triangles just with the addition of the quadrant angles  simply adding 30 45 and 60 to the numbers of 0 90 180 and 270. This activity showed me what was on the outside of the triangle which was in reality the outside of the circle which helped me find the coordinates since the radical 3 over 2 value is always near the x axis.
5. The quadrant that this activity lies in is quadrant one. The values that change if drawn in the different quadrant are the degrees, the value of pie and if the different coordinates are either the x value is negative, the y is negative, or both values are negative. These values change according to the saying of All Students Take Calculus  The A is in the first quadrant which means all values are positive. S is the second quadrant which means sin and csc are positive while everything else is negative. T is in the third quadrant which means tan and cot are positive while everything else is negative. C lies on the fourth quadrant in which cos and secant are positive while everything else is negative.
Inquiry activity reflection
The coolest thing I learned from this activity was that the triangles actually are inside the unit circle.
This activity will help me in this unit because knowing the coordinates on point is really helpful so you don't have to get brain  scattered everywhere.
Something I've never realized about special right triangles and the unit circle is  they connect with each other and relate like a family.

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