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.

Sunday, February 9, 2014

RWA #1: Unit M Concept 4: Parabolas

This picture demonstrates the use of the parabola and how its properties can be used to create monuments

        This video helps in understanding a parabola by first going over the definition. Then by further going into depth in the equal value of the distance from the focus to the vertex. The video then explains the bouncing of distance.

http://www.education.com/study-help/article/pre-calculus-help-conic-sections/

1) The set of all points equal distant to a focus and a special line called the directix (Taken from the video attached to this post)

2)  Key features include the standard form, the direction, the vertex, directrix, focus, axis of symmetry, and value of P

       The formula for parabola is (x-h)^2=4p(y-k) or (y-k)^2=4p(x-h)
          The parabola will vary in direction depending on which variable is squared and the value of P. If x is squared and p is positive the parabola will direct upwards. If P is negative parabola goes down. When y is squared it will go either left or right. While p is positive the parabola goes to the right. While P is negative the parabola goes to the left.
            To find the standard form we can take it from the center value which is the vertex. We can also put together certain pieces if we're not given the vertex. The vertex is found between the focus and directrix on the graph and can be taken from our standard form. The direction is determined by the variables and the value of P. To find our directrix we use fvd and go down or up according to the direction and determined by the value of P. The focus is found the same way. The axis of symmetry is found through when using fvd what value that does change when using fvd such as going dvf  on the graph the y will stay the same because its moving horizontally. Value of P is found through setting the value in front of the non-squared term equal to 4p.
                   The focus of a parabola affects the shape in that if the focus is closer to the parabola its smaller. The focus is also the same distance to any point on the parabola from straight to the directrix is the same value. A parabola's eccentricity is equal to one.
                  The focus x or y value will change accordingly to what other value changes. Such as if the x values change the focus x value will chance. The focus is also in the middle between the vertex on the axis of symmetry. The focus will change in location according to what direction the parabola is facing.

3) Conics of parabolas could be used in many different way in finding the length of bridges, or monuments. Parabolas can be used to determine the waves of satellite dishes in how they the signals are able to bounce back and forth as shown in the video and these signals then bounce towards satellites which receive this signals and project images on television. (Cited from Mrs. Kirch explanation in class)


4) Works cited

  • Mrs Kirch lecture
  • .  http://www.education.com/study-help/article/pre-calculus-help-conic-sections/
  • http://www.mathsisfun.com/geometry/parabola.html
  • http://www.mathwords.com/f/focus_parabola.htm 
  • https://www.youtube.com/watch?v=INYUob0_wjo