Ok I have a few questions for test 1, I'm still all about making an A, and I think I'm really close.
course
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the period is normally just 2pi, correct?
So to get the period we just take 2pi and divide it by whatever is directly in front of x, which would be B. Is this all correct?
Amplitude is just A, and then phase shift is just c/b
All correct so far.
Also when it asks to find the exact value of tan(7pi/12),
what did you say that 7pi/12 is equal to? I""""m still a little confused on how to solve this one. I know this would be equal to 105degrees...
Do you add or subtract 360 degrees until you get the answer?
You know the values of the functions for 7 pi / 6. Use these values and the half-angle formulas.
The other one I wondered about is 1pi/12
I know that this is equal to 30 degrees, which cos and sin values are squareroot of 3/2 and 1/2,
so would the other values just be 1/2 of square root of 3/2 which is what exactly and 1/2 of 1/2 which is 1/4??
No. Gotta use half-angle formulas.
Is it says to list the formulas of sin(a+b)cos(a+b) & tan(a+b).
then you just want,
sin(a+b)=sinacosb+cosasinb
cos(a+b)=cosacosb-sinasinb
tan(a+b)=(tanatanb)/(1-tanatanb)
Right. Good.
The tire of an automobile completes 12 revolutions in a second. The diameter of the tire is 20 inches. How fast is the rim of the tire moving? I am uncertain of how to do this one, will you explain it to me?
12 rev / sec = 12 * circumference / sec. Circumference = 2 pi r.
12 rev / sec = 12 * (2 pi) radians / sec. Multiply radians / sec by radius and get speed.
Establish or refute the proposed identity cos^2(a)( 1 + tan^2(a)) = 1
Here I just just substitute in 1/sec2 for cos 2, correct? and then i could multiply out the sec2, and get the correct answer...
That will probably work if you do it right.
Alternative: Do everything in terms of sines and cosines (tan(a) = sin(a) / cos(a) ).
The average monthly temperatures at a certain location are -1.836204, 4.832054, 19.57578, 38.44833, `y5, 68.61944, 71.8417, 65.20203, 50.47776, 31.61035, 13.65029 and 1.405208 degrees in months 1, 2, 3, …, 12 of the year. Give a model of the form y = A sin(`omega t - `phi) + c for these temperatures.
Ok to get my amplitude I would just find the lowest amount, and the highest and then find how far they lie from the x axis, and then I would know that peaks at the 7th month b/c thats where it is the greatest, and then its the lowest at month 1, but how do I find the phase shift and the period length, especially with that y5 in there...
These values are for a year, and temperature varies periodically over the period of a year. So the period is 12 months.
Amplitude is half the difference between highest and lowest.