SSA is considered an ambiguity because you don't know how many solutions there will be. There could be 0 solutions, 1 solution, or 2 solutions. You can find out how many solutions there are by solving for h. Sin θ = h/a. If h<a<b than you have two solutions. If h>a than there are no solutions. If h=a than you have 1 solution.
After doing the Feeling Trig Functions projects I learned how to graph different types of trig functions on a larger scale. Trig functions were something that I had trouble understanding on paper, but when given the opportunity to learn it hands with this activitey, I grew intellectually much faster. I really benefited from this style of learning and practicing. Somethings I struggled with in the begining with this activity was the unit circle. SInce algebra 2 and precalc I was always able to use a unit circle graph on a quiz or a test. This time around I had to memorize the units on the unit circle. A tactic I used was counting the number units on the x-axis in relation to the unit circle. For example, if the problem was sin(pi/2) I would count how many cards from zero on the x-axis then go to the unit circle and find the point of pi/2. This helped me make connections between the unit circle and trig functions. During the assement portion, I liked that we couldn't consult Mr. Cresswell. It added more of a challenge to the project. Having a partner helped me affirm my reasoning during the activity.
All in all I really enjoyed this hands on activity and would reccomend it for future students.
A radian is a unit of an angle at the center of the circle. The arc's length is equal length to the radius. Radians relate to the unit circle because they can be converted into degree measures around a circle. These measurements help us find the reference angle, the sines, the cosines, and the tangents of a triangle. The circumference of a unit circle is 2pi radians or 360 degrees. With this info we can figure out how many times the radius can go around the circle with the respected amount of radians given. Radians and degrees can be converted to each other. I prefer degrees because it gives you a nice whole number that I can visually see better. Radians tend to be fractions with pi attached to it, making the measurement look gross. However, radians are more mathematically pure.
The following data is cacluated through bankrate.com. We approximated that tution would be $5,000 a year and we assumed that we would finish in four years. Making the total cost $20,000. We googled Government subsidized and unsubsidized student loans. Along with a private bank. Private banks vary so for this blog post we used Citizens Bank.
Government Subsidized Student Loans
Interest Rate: 4.60%
Monthly Pay: 103.25
Total Time: 30 years
Total Interest: $17,170
Government unsubsidized student loans
interest rate: 6.8%
Monthly pay: $119.92
Total Time: 30 years
Total Interest: $26,294.24
Private Bank: Citizens Bank
Interest Rate: 10%
Monthly Pay: 175.52
Total Time: 30 years
Total Interest: 43,168.39
There is roughly 1.513385x10^10 inches from the Earth to the Moon. The equation of folding a standard piece of paper would be .005(2^x). By graphing the equation and the amount of inches to the moon we find that the lines cross at (0, 1.513385x10^10). Which means it would take roughly 1.513385x10^10 folds of the paper. This is unrealistic because one piece of paper would be damaged after every fold. It would be physically impossible to fold it that many times. I think the stack would be so microscopically small, none of us would be able to see it just with the naked eye.
Factors and zeros are inversely related. For example if a polynominal has a factor of (x-3), then a zero of that polynominal would be x=3. Long division can help us find more zeros when graphing can't. The degree of the polynominal can help us predict the number of zeros. If a polynominal's highest degree is x^5 then it would have five solutions. However, that doesn't mean it would have 5 factors because the solutions could be imaginary or irrational. A solution is imaginary when you have to take the square root of a negative number.
-The function above is exponential.