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

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alysa111
 9 months ago
Best ResponseYou've already chosen the best response.0@kelliegirl33 can you help me

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

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

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

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1You can use the draw tool.

alysa111
 9 months ago
Best ResponseYou've already chosen the best response.0dw:1403474666905:dw

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

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

alysa111
 9 months ago
Best ResponseYou've already chosen the best response.0legnth of adjacent / legnth of hyp

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

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

alysa111
 9 months ago
Best ResponseYou've already chosen the best response.0the adjacent side is 20

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1You are correct to say that.

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

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

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.120^2+21^2=c^2 and then take the square root of both sides to give you c.

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

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

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1don't forget the negative sign

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

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1if 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

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1dw:1403475467323:dw

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

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

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

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

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

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1For 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)

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

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

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

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

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

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1Let 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?

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1like 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?

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

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

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1great 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)

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

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1omg 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

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

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1Also 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)

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

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1well 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?

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

alysa111
 9 months ago
Best ResponseYou've already chosen the best response.049 = 5 which is the same for g(x)

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1Ok 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?

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1That 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.

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1For 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.

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1dw: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?

alysa111
 9 months ago
Best ResponseYou've already chosen the best response.0functions has the greatest yintercept

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

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1dw:1403477214481:dw

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

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

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

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

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.1how did you get that?

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

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

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

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

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

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

myininaya
 9 months ago
Best ResponseYou've already chosen the best response.15(1)5 can you simplify from here now?

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

alysa111
 9 months ago
Best ResponseYou've already chosen the best response.01f sin Θ = 15 over 17, use the Pythagorean Identity to find cos Θ.

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

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

alysa111
 9 months ago
Best ResponseYou've already chosen the best response.0dw:1403477725033:dw

alysa111
 9 months ago
Best ResponseYou've already chosen the best response.0dw:1403477767271:dw

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

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

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

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

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

myininaya
 9 months ago
Best 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 \[(\sin(\theta))^2+(\cos(\theta))^2=1 \\ (\frac{15}{17})^2+(\cos(\theta))^2 =1 \text{ I did this because I was given that } \sin(\theta)=15/17\]

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

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

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

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

alysa111
 9 months ago
Best ResponseYou've already chosen the best response.0dw:1403478332917:dw

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

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

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

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

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

alysa111
 9 months ago
Best ResponseYou've already chosen the best response.0dw:1403478613956:dw my only option

alysa111
 9 months ago
Best ResponseYou've already chosen the best response.0In 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).

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