This animated graph was based off of the following equations: r=asinbtheta and r=acosbtheta. I put these two equations into Gifsmos, added sliders, and recorded it.
For the first piece of art, I used the cosine polar graph equation and the sine polar graph equation to create three different flowers. I then used sliders to change the design and the size of the flowers. The different coefficients that are in the sliders, make the design and size of the graph.
In this piece of art, the graphs are based off of r=atheta and r=asinbtheta I used r=atheta to create two different spirals. I used r=asinbtheta to create two flowers. I then used sliders to change the size and design of the flowers and spirals. The different coefficients that are in the sliders, make the design and size of the graph.
For the last piece of art I used Gifsmos.com to create an animation. I used the polar graphs of sine and cosine to make the flowers. I used theta to create spirals. I set 'r' equal to a coefficient to create the circles. I made the spirals opposite of each other. I used sliders and recorded it to create an animation. The different coefficients that are in the sliders, make the design and size of the graph.
*My computer would not save the animation so I recorded it off my phone. Sorry for the bad quality*
The graphs I created at the beginning of the trimester were not as complex as the ones at the end of the trimester. Trig taught me different, yet interesting graphs. It has also taught me how to make more complex graphs.
I used each of the equations from the activity to create each of the following graphs. I used r=acosbtheta, r=asinbtheta, and r=atheta. "a" makes the graph bigger or smaller and b changes the design of the graph.
We have been learning about SSA abiguity the last few days. SSA is ambiguous because there can be more than one triangle. You cannot just apply the law of sines because first you need to determine whether there are two, one, or zero triangles. You need to find the amplitude. If side a is more than side b there is only one triangle. If side a is less than side b and more than the amplitude, there are two triangles. If side a is less than h, there aren't any triangles. If i had to teach someone SSA ambiguity, I would draw diagrams and do example problems.
I didnt realize the unit circle and the graph related. Finding the measure on the unit circle then using the triangles to find out where it goes on the graph helped me understand trig a little better. Everything just made sense. I thought it was kind of challenging not to have the teacher be able to tell us whether it was right or not. It made my partner and I second guess everything.
The difference between sin and cos The period for sin always starts at a midpoint and the period for cos starts at a maximum. Sine can be written as a cosine and vice versa.
tan: amplitude:in period: pi
csc: amplitude: inf period:2pi
*I graphed the csc upside down on accident
sec: amplitude: inf period:2pi
cot: amplitude: infinite period: pi
Asymptotes occur when there is an error in the graph. When there is an error that means it divides by zero.
A radian is a unit of angle that is equal to an angle at the center of the circle in which the arch is equal to the radius. I would tell someone that a radian is an angle measure around a unit circle. At about 180 degrees, the radian measure is one pi. At 360 degrees, the radian measure is 2 pi. The circumference of a circle is 2(pi)(r). In the unit circle one time around the circle is 2pi because the radius is 1. Radians can be converted to degrees and degrees can be converted to radians. They both show a unit of angle measure on the unit circle. I prefer degrees over radians because I think its easier to determine where it is at on the circle. Radians seem more mathematically pure because instead of using a decimal it will be in a fraction. Fractions are easier to deal with than a decimal. Radians are more precise.
I chose cheerleading because I really enjoy it. It taught me responsibility and to never give up. It also taught me to be mentally and physically strong. Cheerleading involves back handsprings, high v's, splits, back tucks etc. Math in cheerleading involves parabolas, rotation, degree of angles, absolute value functions, and more.
Below, is a picture of me doing a high V in desmos. As you can see a high v looks very similar to an absolute value function. I used sliders for b, a, and c. The function is y=|-6+1.2x|+0
This image is of the splits. the angle of my legs on the floor is 180 degrees.
Below is a video of a back handspring and a picture of the arch in a back handspring in desmos. The arch of a back handspring looks like a upside down parabola. I used sliders for a, b, and c. The function of the arch is y=-0.5x^2+3.5x-2.
Below is a video of my friends and I doing a back tuck. We jump up, and at the peak, we tuck our legs, and rotate 360 degrees back on our feet.