Section 4 (Trig. Fcns. of any Angle)
Nov 6th, 2010 by corricelli
Hello Teams 2 and 7,
Let’s use this spot to post questions for Honors Precalculus, Unit 4, Section 4!
Happy blogging,
Mrs. Corricelli
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I’ve having trouble on number 31 on tonight’s homework. So far I know the given, which makes y=0. I’m not exactly sure where to go after that. Can someone help please?
Ok, on number 9 b, I used the point (-8, 15) in order to find the hypotenuse, which is 17. Maybe im putting the triangle in the wrong place but when i do sin of theta (is that right?) I put opposite over hypotenuse and i get -8/17 but the book says that this is the cosine, and sine is 15/17 so what am I doing wrong?
Jen-
Check out the example from today in class that similarly has an undefined cos. I think that will help you. Its example 2
Anyone do the last problem yet? I’m having some troublesss
Becca, you’re switching the x and the y’s.
sine= opposite/ hypotenuse= y/ radius= 15/17
cos= adjacent/ hypotenuse= x/radius= -8/17
tan= opposite/ adjacent= y/x
thanks mariah, i think im just looking at the triangle wrong! yayy!
rachel
for the last quetion (93 )
I drew a triangle in the 1st quadrant and the 3rd quadrant. Starting in the 1st quadrant, csc(theta) is the same as the inverse of sign, so i just flipped 2sqrt3/3 so that it became sin(3/2sqrt3) Then since sine is opp./hypot. the y-value would be 3 and the radius (hypotenuse) would be 2sqrt3. So then i did the pythag. theorem and i got the x value to be sqrt3. So then its a 30-60-90. sqrt3=x, xsqrt3=sqrt3 x sqrt3, and 2x= sqrt 3=2sqrt3. Then you do the same thing for the third quadrant.
i mean do the same thing in quadrant 2
I KEEP FORGETTING TO PUT IN THE SPAM WORD UGH! SO IVE WRITTEN THIS LIKE FOUR TIMES.
for number 31 I think i figured it out
you are given that cot of theta is undefined
so our y value must be 0, meaning (x,0) of the point were trying to find is known so far
based on the constraints of theta, it must be greater than pi/2 and less than 3pi/2 which means it must be in the 2 or 3 quadrant, so your x value must be negative. so (-x,0) is known so far
Now the example problem we did in class used the rotation of pi/2 to find where a point was, so I looked in the book
according to the book there are four quadrant angles, each with a point
0, with point (1,0)
pi/2, with point (0,1)
pi, with point (-1,0)
and 3pi/2, with point (0,-1)
the only point with a negative x is the quadrant angle pi, which fits into the constraints on theta
so the point I found was (-1,0) which I then plugged in to find its functions and all that jazz.
It could be wrong, but it got me there
Thanks lauraaa!!
hey guys! so on number 99 in the homework, how would you plug all the different variables into the regression feature?
yeah michaela i’m having the same problem. i think you’re supposed to use the SinReg feature in the STAT button, but i keep getting an error in the calculator and changing the mode from degrees to radians didn’t help so i still don’t know what to do
Ok guys, Taylor and I looked this up online so here we go.
Steps:
1.click stat
2.go to edit
3.enter your data in Lsub1 Lsub2 and Lsub3 (aka months and then New York and Alaska stuff)
4.click stat
5.calc
6.sin reg
7.second, Lsub1 comma Lsub2 comma Ysub1
8.enter
9. find values and plug into equation
I am not completely sure how to get the Ysub1 in anymore but this is what worked for me.
P.S. can anyone help me with 101 b and c?
Can someone help me with 99b? I’m not sure what I’m doing wrong.
The regression formula I have for New York is
y= 22.098 times sin (0.522t-2.219) + 55.008
and for Fairbanks I have
y= 34.997 times sin (0.499t-1.839) + 26.468
For b I understand we have to plug in the other months as t, right? When I plug it in I get numbers that are really close together, and it ends up being that the original values (like for January, April, etc.) don’t match the ones on the table in the book either.
Jen, I have no clue… maybe it’s something about the mode?
We should ask her that one… I’ll be skipping it for now until something enlightening happens
Ah the changing the mode into radians instead of degrees works! Thanks Mariah!
jen, check your mode! i’m in radians and functions.
and i did it one at a time, then plugged it into y= with three sig figs/ decimal places, and it came out right.
Thanks again Mariah!
Becca, for 101 b and c I think we are plugging in the values they give us for t into the equation
y (t) = 2e^-t times cos 6t
And e^ is 2nd LN on the graphing calculator
There’s no 4.5 page, but I’m having trouble understanding how b affects the graph, especially when b= something with pi.
Hey Mariah,
this is my attempt to explain B…
B represents the period. In a sinosoidal curve, the period is the amount of ‘time’ it takes for the curve to repeat. It determines whether the curve will be horizontally stretched (the curves are more stretched out) or a horizontal shrink (the curves are tighter together). Because the mini formula to get period is 2pi/b, if b is between 0 and 1, te graph will stretch horizontally.
Ex. B=.5. 2pi/.5= 4pi. This is a larger number than 2pi and there fore it will take longer for the curves to repeat, resulting in a stretch. When b is greater than one, the period will be less than 2pi, creating more cramped curves, and a horizontal shrink. Hope this helps.