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alysa111
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For an angle Θ with the point (−20, −21) on its terminating side, what is the value of cosine?
 5 months ago
 5 months ago
alysa111 Group Title
For an angle Θ with the point (−20, −21) on its terminating side, what is the value of cosine?
 5 months ago
 5 months ago

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alysa111 Group TitleBest ResponseYou've already chosen the best response.0
@kelliegirl33 can you help me
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
If it helps you graph the point. Can you do that for me first?
 5 months ago

alysa111 Group TitleBest ResponseYou've already chosen the best response.0
@myininaya just plot 20,21 ?
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
Yep plot the point as a first step.
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
You can use the draw tool.
 5 months ago

alysa111 Group TitleBest ResponseYou've already chosen the best response.0
dw:1403474666905:dw
 5 months ago

alysa111 Group TitleBest ResponseYou've already chosen the best response.0
@myininaya
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
dw:1403474755600:dw Now I will simply make a right triangle using the center of the graph for my central angle.
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
what is the ratio definition of cosine of an angle?
 5 months ago

alysa111 Group TitleBest ResponseYou've already chosen the best response.0
legnth of adjacent / legnth of hyp
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
right you already have the adjacent side given in the picture the only thing you need now is the hyp of that triangle, right?
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
Find the hyp of that triangle using Pythagorean Theorem.
 5 months ago

alysa111 Group TitleBest ResponseYou've already chosen the best response.0
the adjacent side is 20
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
You are correct to say that.
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
Can you find the length of the hyp?
 5 months ago

alysa111 Group TitleBest ResponseYou've already chosen the best response.0
yes hold on wouldnt it be 20^2 + 21^2 = c^2
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
20^2+21^2=c^2 and then take the square root of both sides to give you c.
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
so that is the length of the hyp so what is cos(theta)=?
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
you said earlier cos(theta) is adj/hyp you never said cos(theta) is hyp
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
don't forget the negative sign
 5 months ago

alysa111 Group TitleBest ResponseYou've already chosen the best response.0
thank you so much i have a few more cn yu help me
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
if the angle was on the side of the graph like on the right hand side of the yaxis cos would have been indeed a positive number but since the angle was to the left of the yaxis cos will be negative
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
dw:1403475467323:dw
 5 months ago

alysa111 Group TitleBest ResponseYou've already chosen the best response.0
How does changing the function from f(x) = 3 sin 2x to g(x) = 3 sin 2x + 5 affect the range of the function?
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
we could even talk about sine sin is positive when above the xaxis and sine is negative when below the xaxis dw:1403475522177:dw
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
Well you are talking about shifting the graph up when you have that +5
 5 months ago

alysa111 Group TitleBest ResponseYou've already chosen the best response.0
so the function shifts up 5 units so the range changes from 1 to 1
 5 months ago

alysa111 Group TitleBest ResponseYou've already chosen the best response.0
in f(x) to 4 to 6 in g(x)
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
For example, pretend we have y=sin(x) the range of sin(x) is from 1 to 1 (inclusive). but when we look at y=sin(x)+1 that means you are moving every point of y=sin(x) up one unit so the range of sin(x)+1 is from 1+1..1+1( inclusive) doing the addition gives 0..2 (inclusive)
 5 months ago

alysa111 Group TitleBest ResponseYou've already chosen the best response.0
am i right
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
well first what is the range of y=3sin(x)?
 5 months ago

alysa111 Group TitleBest ResponseYou've already chosen the best response.0
f(x) = 3 sin 2x to g(x) = 3 sin 2x + 5 affect the range of the function
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
yes the range of the graph of f would be affected if you need f+5
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
did f+5 (not need)
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
but the range of y=3sin(x) is not 1 to 1.
 5 months ago

alysa111 Group TitleBest ResponseYou've already chosen the best response.0
Which of the following functions has the greatest yintercept?dw:1403475803380:dw
 5 months ago

alysa111 Group TitleBest ResponseYou've already chosen the best response.0
its 2 to 8
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
Let y=sin(x). Let f(x)=3sin(x). Therefore you could say f(x)=3y where y=sin(x). If you have 3 times every y per x wouldn't the range be stretched more?
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
like the range for y=sin(x) is 1 to 1 (when we talk about range we are talking about the y values) the lowest y value for y=3sin(x) would be what then?
 5 months ago

alysa111 Group TitleBest ResponseYou've already chosen the best response.0
so f(x) has greater yintercerpt
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
the lowest y value for y=sin(x) is 1 so the lowest y value for f(x)=3sin(x) is ?
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
great so it shouldn't be hard for you to see the highest yvalue for f(x)=3sin(x) would be 3(1)=3 so the range for y=3sin(x) is 3 to 3 (inclusive)
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
now what is the range for y=3sin(x)+5
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
omg you are great so now you can answer that one question about how the range is affected and actually state the ranges of both functions
 5 months ago

alysa111 Group TitleBest ResponseYou've already chosen the best response.0
now for Which of the following functions has the greatest yintercept? wouldnt it be f(x) since the y is 9
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
Also when answering the question it might be better to choose to answer in interval notation or inequality notation. 2 to 8 isn't really something people say to state an interval (not that I have ever seen anyways)
 5 months ago

alysa111 Group TitleBest ResponseYou've already chosen the best response.0
Okay , so it would be stated has 2 to 8 in g(x)
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
well like i said you might want to choose to answer in interval notation (or inequality) y is an element of the interval [2,8] <interval (i put brackets to mean to included endpoints inequality notation: \[2 \le y \le 8\] and to your next question.... dw:1403476409004:dw do you what the yintercept is for a curve? It is the part of the curve that goes through the yaxis. When I say part, I'm talking about the specific point in which the curve does that. What do you know about all the points on the yaxis? What do they all have in common?
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
I will give you a hint. All the x values of any point on the yaxis are _____?___
 5 months ago

alysa111 Group TitleBest ResponseYou've already chosen the best response.0
Im not sure
 5 months ago

alysa111 Group TitleBest ResponseYou've already chosen the best response.0
49 = 5 which is the same for g(x)
 5 months ago

alysa111 Group TitleBest ResponseYou've already chosen the best response.0
the same yintercept
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
Ok since you can't answer that, I will ask you a series of questions now? Where does (0,10) lie? Where does (0,5) lie? Where does (0,2) lie? Where does (0,0) lie? Where does (0,1) lie? Where does (0,6) lie? where does (0,1000) lie?
 5 months ago

alysa111 Group TitleBest ResponseYou've already chosen the best response.0
on the x axis
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
That is incorrect. They all lie on the yaxis. The answer to my question: All the xvalues of any point on the yaxis is ____?__ All the xvalues of any point on the yaxis is zero. So to find the yintercept for a curve you just need to find y when x is zero. You just need to replace x with zero and solve for y.
 5 months ago

alysa111 Group TitleBest ResponseYou've already chosen the best response.0
so 09 ? 04 ?
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
For the one function, it should be clear (0,0) is the yintercept (that is the origin of the graph after all; is is all an xintercept) The other function you did right even though it doesn't seem you know why you were doing it since you were not able to answer the question.
 5 months ago

alysa111 Group TitleBest ResponseYou've already chosen the best response.0
Yeah im confused now
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
dw:1403477105487:dw This is the information given. You are asking to find the yintercept for both graphs right? Can you tell me which point from f have the x is 0?
 5 months ago

alysa111 Group TitleBest ResponseYou've already chosen the best response.0
functions has the greatest yintercept
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
I'm asking you to tell which of the points from f have the x value is 0?
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
dw:1403477214481:dw
 5 months ago

alysa111 Group TitleBest ResponseYou've already chosen the best response.0
its 0,0 ?
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
dw:1403477221682:dw Do you see any of these x's being 0?
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
yes the point (0,0) is a yintercept because the x is 0
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
now we need to look at g(x)=5cos(3x)5
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
what point on g gives us the x is 0?
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
how did you get that?
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
Did you replace the x with 0 to see what y is? Because y is not 5 when x is 0.
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
I only care about when x is 0 since you are asking about the yintercept.
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
Replace the x with 0 like so yintercept of g is g(0)=5cos(3*0)5
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
evaluate 5cos(3*0)5
 5 months ago

alysa111 Group TitleBest ResponseYou've already chosen the best response.0
5cos(0)5 5cos
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
you are right to say 5cos(3*0)5 can be wrriten as 5cos(0)5 but where do we go from there?
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
:( 5cos(0)5 what is cos(0)?
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
5(1)5 can you simplify from here now?
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
right so the yintercept for g is (0,0) as well they have the same yintercept
 5 months ago

alysa111 Group TitleBest ResponseYou've already chosen the best response.0
1f sin Θ = 15 over 17, use the Pythagorean Identity to find cos Θ.
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
draw a right triangle using this information sin(theta)=15/17
 5 months ago

alysa111 Group TitleBest ResponseYou've already chosen the best response.0
\[\sin^2 \theta + \cos ^2\theta = 1\] will be what we use ?
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
you can use that
 5 months ago

alysa111 Group TitleBest ResponseYou've already chosen the best response.0
dw:1403477725033:dw
 5 months ago

alysa111 Group TitleBest ResponseYou've already chosen the best response.0
dw:1403477767271:dw
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
if you want to use that specific identity you can replace sin(theta) with 15/17 and solve for cos(theta)
 5 months ago

alysa111 Group TitleBest ResponseYou've already chosen the best response.0
sin(15) = 0.650
 5 months ago

alysa111 Group TitleBest ResponseYou've already chosen the best response.0
sin*17) = 0.96
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
can you replace sin(theta) with 15/17 in the following equation \[\sin^2(\theta)+\cos^2(\theta)=1\]
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
why not?
 5 months ago

alysa111 Group TitleBest ResponseYou've already chosen the best response.0
well wouldnt you put them in front of sin and cos
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
just so you know \[\sin^2(\theta)\] and \[(\sin(\theta))^2\] have exactly the same meaning
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
you are given sin(theta) is 15/17 so you replace the whole sin(theta) thing with 15/17
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
\[\sin^2(\theta)+\cos^2(\theta)=1 \text{ means exactly that } (\sin(\theta))^2+(\cos(\theta))^2=1\] So we have \[(\sin(\theta))^2+(\cos(\theta))^2=1 \\ (\frac{15}{17})^2+(\cos(\theta))^2 =1 \text{ I did this because I was given that } \sin(\theta)=15/17\]
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
now solve for cos(theta)
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
if that confuses you solve the following equation for u \[(\frac{15}{17})^2+u^2=1 \]
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
whatever value(s) you get for u is your answer since u is cos(theta)
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
and cos(theta) is the objective
 5 months ago

alysa111 Group TitleBest ResponseYou've already chosen the best response.0
dw:1403478332917:dw
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
so what did you do to get that?
 5 months ago

alysa111 Group TitleBest ResponseYou've already chosen the best response.0
found cos of theta
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
you solve the equation (15/17)^2+u^2=1 for u (which is cos(theta) )?
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
you might want to do that one more time
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
the denominator is right but your numerator is off
 5 months ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
ok so cos could either be 8/17 or 8/17 when sin is 15/17
 5 months ago

alysa111 Group TitleBest ResponseYou've already chosen the best response.0
dw:1403478613956:dw my only option
 5 months ago

alysa111 Group TitleBest ResponseYou've already chosen the best response.0
In Shadow Bay in July, high tide is at 1:30 pm. The water level is 4 feet at high tide and 0 feet at low tide. Assuming the next high tide is exactly 12 hours later and the height of the water can be modeled by a cosine curve, find an equation for Shadow Bay's water level in July as a function of time (t).
 5 months ago

alysa111 Group TitleBest ResponseYou've already chosen the best response.0
okay so i got f(t) = 4cos pie/2t +1
 5 months ago

alysa111 Group TitleBest ResponseYou've already chosen the best response.0
@myininaya
 5 months ago
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