MHB Couple of hard trig questions....

  • Thread starter Thread starter Sabrina102
  • Start date Start date
  • Tags Tags
    Couple Hard Trig
AI Thread Summary
The discussion revolves around solving several trigonometry-related problems. The first question involves determining the vertical shift, c, in a sinusoidal equation based on given inflation rates. The second question asks for the duration it takes for the moon to return to a full moon and the corresponding period, k. The third question explains why circles of different radii have the same number of radians, while the fourth discusses how multiplying by values greater or less than one affects the period of trigonometric functions. The final question requires identifying intervals of positive, negative, and zero average rates of change for a specific sinusoidal function.
Sabrina102
Messages
1
Reaction score
0
Hi, I was hoping to get some help on these five questions, I've been stuck on these and any help would be greatly appreciated!

1. Inflation rises and falls in a cyclical manner. If inflation is highest at 4.8% and lowest at 1.3%, what c for the equation y = a sin(k(x + d)) + c?
2. If the moon changes from a full moon to a half moon in 13 days, how many more days does it take for it to get back to a full moon and what would the period, k, equal?
3. Explain why a circle of radius 4 cm and a circle of radius 13 m have the same number of radians?
4. Explain why when you multiply by a number greater than 1 inside the argument of a trigonometric function, the period of the function decreases and when you multiply by a number less than 1, the period increases.
5. For the function y = 4sin (pi/ 4 x - pi/2 ) - 3 list when the average rate of change is positive, negative, and zero, considering the beginning of the interval to be x = 4.
 
Mathematics news on Phys.org
Hello, and welcome to MHB! (Wave)

1.) I would begin by stating:

$$-1\le\sin(k(x+d))\le1$$

$$-|a|\le |a|\sin(k(x+d))\le |a|$$

$$-|a|+c\le |a|\sin(k(x+d))+c\le |a|+c$$

And so, from the information given in the problem regarding the minimum and maximum values of inflation the sinusoid is modelling, we must have:

$$c+|a|=4.8\%$$

$$c-|a|=1.3\%$$

Add these equations, and then solve for \(c\)...what do you find?
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Back
Top