Inquiry Activity Summary
The hypotenuse is always labeled r. The verticle value is y and horizontal x. The value for the hypotenuse is 2, x value is radical 3 and the y value is 1. To make the hypotenuse equals to , divide everything by 2.
This triangle is the same, however the angle is in a different position. The x,y,r is label the same with the values. However, the ordered pairs will be in different.
The special right triangle of the 45,45,90 will have a different value. The label of the x,y and r will be the same. To derive it, we need to find the value of each angle. Since 90 degrees value is radical 2 and we want it equal to 1, we must divide everything by radical 2. Since the other angle is being divided by radical 2 we must rationalize it because the bottom can't have a radical number.
This activity help me derive the unit circle because the unit circle is basically made up of the special right triangles including the 45,45,90 degrees and 30,60,90 degrees.
The value of these triangle changed when it is drawn in the second, third, and fourth quadrant by the negative and positive signs
In the second quadrant it is still in the first half, which is positive but it is in the left side. Therefore the x value will be negative while the y value is positive.
The third quadrant is in the bottom half. Because it is on the bottom and to the left, both the x and y value will be negative
Finally, the value of the x and y in the fourth quadrant will be positive and negative. The x is positive and the y is negative because you are starting from the right side of the unit circle and going down.
Conclusion
The coolest thing I learn from this activity is that the unit circle is derive from the special right triangle
This activity will help me in this unit because I did not have to memorize a lot of thugs because I can work out the problems.
Something that I never realize about the special right triangle and the unit circle is that they are both related to each other in many ways
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