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Mathematics 21 Online
Nicole:

http://prntscr.com/nqy5xd

Nicole:

@Vocaloid

Nicole:

@Narad

Narad:

Yes

Nicole:

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Narad:

yes

Nicole:

http://prntscr.com/nqybg0

Narad:

Yes

Nicole:

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Narad:

Yes

Nicole:

http://prntscr.com/nqyc7r

Narad:

All ok

Nicole:

http://prntscr.com/nqycdf

Narad:

All ok

Nicole:

http://prntscr.com/nqycu6

Nicole:

http://prntscr.com/nqydq2

Nicole:

http://prntscr.com/nqyf07

Nicole:

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Nicole:

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Nicole:

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Nicole:

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Nicole:

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Nicole:

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Nicole:

http://prntscr.com/nqyjb2

Nicole:

@Narad can you please tell me what those answers were for those questions please?^

Nicole:

because it isnt there anymore

Narad:

Which one?

Nicole:

you answered them before I just dont see the answers anymore

Narad:

Thet have been removed

Narad:

1st one \[sinB= 0.88\] The angle is \ From my calculator, B=1.08

Narad:

2nd question \[tanB=0.34\] Therefore, the angle is \ From my calculator, B=0.33 rad

Narad:

3rd question \[cosA=0.23\] So, the angle is \[A=\cos ^{-1}(0.23)\] From my calculator, the angle is A=1.34 rads

Narad:

4th question sinB= 11/18 so, the angle is \ From my calculator, the angle is B= 37.67º

Narad:

5th question From the drawing \[sinA=2/4=1/2\] Therefore, the angle is \[A= \sin ^{-1}(0.5)\] From , the unit circle A=30º

Narad:

6th question From the given triangle, by applying Pythagoras theorem \[AB ^{2} = AC ^{2} +BC ^{2}\] AC=5 BC=4 Therefore \[AB ^{2}= 5^2+4^2 =25+16=41\] so, \[AB=\sqrt{41}=6.40\]

Narad:

7th question From the triangle XYZ, \[\tan50º = YZ/XZ\] but, XZ= 6.1 therefore, \[YZ=XZ*\tan50º\] \[YZ=6.1*\tan50º = 7.27\]

Narad:

8th question In the triangle ABC, we have \[tanA=BC/AC\] BC= 4 AC= 5 Therefore, \[tanA=4/5=0.8\] And the angle is \[A= \tan ^{-1}(0.8)= 38.66º\]

Narad:

9th question From the drawing \[\tan50º=x/50\] Therefore, \[x=50*\tan50º= 59.59\] The height of the building is \[H= 5+x=59.59+5=64.59 ft\]

Narad:

10th question The ladder makes an angle of 45º and is 7 ft from the wall Therefore, we have an isoceles triangle By the Pythagoras theorem, The length of the ladder is \[l=\sqrt{7^2+7^2} = 9.90m\] You can also use sin or cosine

Nicole:

http://prntscr.com/nr21ne

Nicole:

@Narad

Narad:

The function to be graphed is \[f(x)=\sin(x)-5\] When x=0, \[f(0)=\sin(0)-5=-5\] When \[x=\pi\], \[f(\pi)=\sin(\pi)-5=-5\] When \[x=\pi/2\], \[f(\pi/2)=\sin(\pi/2)-5=1-5=-4\] When \[x=-\pi/2\], \[f(-\pi/2)=\sin(-\pi/2)-5=-6\] The domain is \[=\mathbb{R} \] The range is\[y \in [-6,-4]\]

Nicole:

Okay but how would it look graphed?

Narad:

1 attachment
Narad:

1 attachment
Nicole:

Hmm I cant see it?

Narad:

\[-1\le sinx \le 1\] \[-1-5\le sinx-5\le1-5\] \[-6\le f(x)\le-4\] This is the range

Nicole:

no im just asking like it says we also have to graph it so can you show me how?

Narad:

You calculate all the points by an incrementation of pi/2 x= -5pi, -4.5pi, -4.0pi, -3.5pi, -3.0pi, -2.5pi, -2.0pi, -1.5pi, -1.0pi,-0.5pi,0, 0.5pi, 1pi,1.5pi.2pi, 2.5pi. 3.0pi, 3.5pi,4.0pi, 4.5pi,5pi you calculate all the point y= f(x)=sin(x)-5 And you plot the curve

Narad:

1 attachment
Nicole:

but it says graph by radians?

Nicole:

@Narad ?

Narad:

The maximum are at (-7pi/2,-3pi/2, pi/2, 9pi/2) The minimum are at (-5pi/2, -pi/2,3pi/2,11pi/2)

Nicole:

okay but how can I graph it on this graph: http://prntscr.com/nr3adh

Nicole:

@Vocaloid some input please

Nicole:

@Narad the next question is :http://prntscr.com/nr4ch4

Nicole:

domain and range? @Narad

Narad:

Narad:

The graph is as the attachement. The domain is all real numbers \[-1\le cosx \le1\] \[-2\le 2cosx \le2\] The range is\[ y \in [-2, 2]\] The maxima are at (-4pi, -2pi, 0, 2pi, 4pi) The minima are at (-3pi, -pi, pi, 3pi)

Nicole:

http://prntscr.com/nr4w2w

Nicole:

@Narad

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