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anonymous
 3 years ago
If tanΘ= 4/3 and Θ lies in the second quadrant, then sinΘ2cosΘ=?
anonymous
 3 years ago
If tanΘ= 4/3 and Θ lies in the second quadrant, then sinΘ2cosΘ=?

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anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0sinΘ2cosΘ = (sin Θ/ cos Θ) (2cos Θ/cosΘ) = tan Θ  2 = 4/3  2 = ???

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0why we need to divided by cosΘ??

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1you can't just divide by cos theta, you need to multiply also.

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1i would suggest you find sec theta first, from the identity sec^2 theta = 1+ tan^2 theta and then, cos = 1/ sec, sin = tan * cos.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0i have learnt sec yet, i have learnt sin cos tan only so far

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1365910549853:dw

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0there is a picture of an angle whose tangent is \(\frac{4}{3}\)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0you need the third side, which you get via pythagoras or by remembering the 3  4  5 right triangle

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1365910630356:dw

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0now you see that \(\sin(\theta)=\frac{4}{5}\) and \(\cos(\theta)=\frac{3}{5}\) except that since you are in quadrant II you have \(\cos(\theta)=\frac{3}{5}\) because in quadrant II cosine is negative

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0you want \[\sin(\theta)2\cos(\theta)\] and you know the numbers that you need \[\frac{4}{5}2\times (\frac{3}{5})=\frac{4}{5}+\frac{6}{5}\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0rather easy if you draw a triangle otherwise a pita

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1Alternate way to look at the same thing, dw:1365910821672:dw so the angle inside triangle is \(\pi  \theta\) so, \(\cos(\pi\theta)=3/5, \cos \theta=3/5 , \cos \theta = 3/5\)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0thank you both of you

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0and the next questions is : [1/cosθ + tanθ](1sinθ)=?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0i got the answer cosθ but there are only five choices: A. sinθ B. cosθ C. cos^(2)θ D. 1+sinθ E. sinθtanθ

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1how you got cos theta ?

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1more specifically, how you got that  *minus*

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[(\frac{1}{a}+\frac{b}{a})(1b)=\frac{1b^2}{a}\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[\large \tan \theta=\frac{4}{3}\] \[\large \theta =126`52'\] \[\sin \theta 2cos\theta=\sin 126`52' 2\cos126`52'\] \[\large =2\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0in this case \(a=\cos(\theta)\) and \(b=\sin(\theta)\) so you get \[\frac{1\sin^2(\theta)}{\cos(\theta)}\] since \(1\sin^2(\theta)=\cos^2(\theta)\) you end up with \[\frac{\cos^2(\theta)}{\cos(\theta)}=\cos(\theta)\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1365911248263:dw

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0ummm, may be i got something wrong

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0the algebra is easier if you put \(\cos(\theta)=a\) and \(\sin(\theta)=b\)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0then you won't get so confused when you multiply stuff out almost all the steps are algebra, there is very little trig here

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[(\frac{1}{\cos(\theta)}+\tan(\theta))(1\sin(\theta))\] becomes the more simple to compute \[(\frac{1}{a}+\frac{b}{a})(1b)\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0or if you prefer \[(\frac{1+b}{a})(1b)\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0now you get \(\frac{1b^2}{a}\) almost instantly

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0ohhh, i write sin^(2)θ1 ....

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0actually \(1\sin^2(\theta)\) for the numerator

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0i want to ask (1+sinθ)(1sinθ)=1sin^(2)θ??

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0ohhhh...then the answer is cosθ

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0and the next question: If cosθ=1/k and 0°≤θ≤90°, then tan(90°θ)=?

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1dw:1365911889934:dw find the unknown side by using pythagoras theorem ?

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1dw:1365911994361:dw now find (tan 90theta) = opposite side / adjacent side

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1sorry, that should read \(\large k^21\)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0tan(90theta)=1/tan theta?

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1you can use that identity , its just another way to solve the same problem.

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1you'll get the same answer using any of the 2 methods.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[\frac{ 1 }{ \sqrt{k ^{2}}1 }\] ??

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.1if you meant , \(\Large \frac{ 1 }{ \sqrt{k ^{2}1} }\) then you are correct.
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