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anonymous
 one year ago
5(cos^2)60 + 4(sec^2)30  (tan^2)45 = x
Find x
anonymous
 one year ago
5(cos^2)60 + 4(sec^2)30  (tan^2)45 = x Find x

This Question is Closed

freckles
 one year ago
Best ResponseYou've already chosen the best response.2well cos(60) and sec(30) and tan(45) can all be evaluated using the unit circle

freckles
 one year ago
Best ResponseYou've already chosen the best response.2http://buildingaunitcircle.weebly.com/uploads/6/2/2/3/622393/9409299.gif

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Use the trig table........

freckles
 one year ago
Best ResponseYou've already chosen the best response.2do you need help using that chart above ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0.... I need to the values like cos = 1/2 and all.......

freckles
 one year ago
Best ResponseYou've already chosen the best response.2cos(60)=1/2 that is correct so squaring both sides gives cos^2(60)=1/4

freckles
 one year ago
Best ResponseYou've already chosen the best response.2sec(30) means you need to find cos(30) and flip whatever number that is

freckles
 one year ago
Best ResponseYou've already chosen the best response.2tan(45) means you need to find sin(45) and cos(45) but both sin(45) and cos(45) are the same so tan(45)=1

freckles
 one year ago
Best ResponseYou've already chosen the best response.2\[5 \cos^2(60)+4\sec^2(30)\tan^2(45) \\ 5(\frac{1}{4})+4(\frac{1}{\cos(30)})^21\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.2so you still need to find cos(30)

freckles
 one year ago
Best ResponseYou've already chosen the best response.2\[\cos(30)=\frac{\sqrt{3}}{2} \\ \cos^2(30)=\frac{3}{4} \\ \frac{1}{\cos^2(30)}=\frac{4}{3} \\ \sec^2(30)=\frac{4}{3}\] that is right so far you have this now: \[5(\frac{1}{4})+4(\frac{4}{3})1\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.2that can be simplify just be doing a few multiplications and additions(subtractions)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ 5 }{ 4 } +\frac{ 16 }{ 3 }  1\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.2yes which the lcm(4,3,1)=12

freckles
 one year ago
Best ResponseYou've already chosen the best response.2\[\frac{5}{4}+\frac{16}{3}\frac{1}{1} \\ \frac{5(3)}{4(3)}+\frac{16(4)}{3(4)}\frac{1(12)}{1(12)} \\ \frac{5(3)}{12}+\frac{16(4)}{12}\frac{12}{12} \\ \frac{5(3)+16(4)12}{12}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.2and totally correct :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thanks! Please help me a bit more?

freckles
 one year ago
Best ResponseYou've already chosen the best response.2Sure. I can take a stab at it.

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0@freckles would using identities just take longer?

freckles
 one year ago
Best ResponseYou've already chosen the best response.2@triciaal if you want to try something with identities you can

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ cotA1 }{ 2 \sec^2(A) } = \frac{ \cot A }{ 1 + tanA }\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.2some people don't need to put in terms of sin and cos but I always do because I remember more identities with sin and cos

freckles
 one year ago
Best ResponseYou've already chosen the best response.2\[\frac{\frac{\cos(a)}{\sin(a)}1}{2\frac{1}{\cos^2(a)}} =\frac{\frac{\cos(a)}{\sin(a)}}{1+\frac{\sin(a)}{\cos(a)}}\] so this is what I would do as a first step second step would be to remove the compound fraction action going on

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm suppose to use LHS and get RHS

freckles
 one year ago
Best ResponseYou've already chosen the best response.2ok then get rid of the compound fraction action on the the left hand side

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ \cos(a)  \sin(a) }{ \sin(a) }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and for the denominator 2sin^(a)/cos^2(a)

freckles
 one year ago
Best ResponseYou've already chosen the best response.2\[\frac{\frac{\cos(a)}{\sin(a)}1}{2\frac{1}{\cos^2(a)}} \cdot \frac{\sin(a) \cos^2(a)}{\sin(a)\cos^2(a)} \\ \frac{\cos^3(a)\cos^2(a)\sin(a)}{2 \cos^2(a)\sin(a)\sin(a)} \\ \text{ so doing a bit of factoring } \\ \frac{\cos^2(a)(\cos(a)\sin(a))}{\sin(a)(2 \cos^2(a)1)} \\ \\ \text{ now recall on the other side we wanted } \cot(a) \\ \text{ on \top } \\ \text{ well we notice } \frac{\cos(a)}{\sin(a)}=\cot(a) \\ \cot(a) \frac{\cos(a)(\cos(a)\sin(a))}{2 \cos^2(a)1} \\ \] now somehow we have to show that \[\frac{\cos(a)(\cos(a)\sin(a))}{2 \cos^2(a)1}=\frac{1}{1+\tan(a)}\] any ideas @BlackDranzer

freckles
 one year ago
Best ResponseYou've already chosen the best response.2if not read this if you want spoilers: \[\frac{\cos(a)(\cos(a)\sin(a))}{2 \cos^2(a)1} \cdot \frac{\cos(a)+\sin(a)}{\cos(a)+\sin(a)} \\ \frac{\cos(a)(\cos^2(a)\sin^2(a))}{(2 \cos^2(a)1)(\cos(a)+\sin(a))} \\ \text{ well recall double angle identity for } cosine \\ \frac{ \cos(a)}{\cos(a)+\sin(a)}\] now divide both top and bottom by cos(a)

freckles
 one year ago
Best ResponseYou've already chosen the best response.2that is I used \[\cos(2a)=\cos^2(a)\sin^2(a) \\ \text{ and also } \cos(2a)=2\cos^2(a)1\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.2yep and we can bring down that cot(a) factor we had from earlier (though I normally write my fractions like this 1/(1+tan(a)) )

freckles
 one year ago
Best ResponseYou've already chosen the best response.2so the key in our proof was the use of double angle identity for cosine

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Nice.. Thanks... I need help in quadratic equations too...

freckles
 one year ago
Best ResponseYou've already chosen the best response.2hey @triciaal did you come up with a way using identities for the first one ?

freckles
 one year ago
Best ResponseYou've already chosen the best response.2I honestly haven't given it a try

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0An aero plane flying at 1 km horizontally above the ground make an angle of elevation 60 after 10 seconds its 30 find the speed of the aerplane in km/hr

freckles
 one year ago
Best ResponseYou've already chosen the best response.2wait what does that mean what is the angle of elevation 60 or 30?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0from 60 to 30 in secs from the smae point

freckles
 one year ago
Best ResponseYou've already chosen the best response.2oh the angle of elevation changed from 60 to 30 in 10 sec gotcha

freckles
 one year ago
Best ResponseYou've already chosen the best response.2dw:1436680212196:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.2so to find the speed of the airplane over that 10 sec we will need to find the distance it traveled for both angle of elevations...

freckles
 one year ago
Best ResponseYou've already chosen the best response.2dw:1436680529581:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.2wait my drawing is off

freckles
 one year ago
Best ResponseYou've already chosen the best response.2I will just make two separate drawings dw:1436680577539:dw dw:1436680738212:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.2We need to find the distance the plane has flown for both pictures

freckles
 one year ago
Best ResponseYou've already chosen the best response.2notice that is x for the first drawing and B for the second drawing

freckles
 one year ago
Best ResponseYou've already chosen the best response.2then once you find the distances for both pictures you will find the difference of those distances and that resulting distance/10 secs will be the speed of the airplane in that 10 secs you have that change

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0How to find the dist?

freckles
 one year ago
Best ResponseYou've already chosen the best response.2you can use a trig ratio

freckles
 one year ago
Best ResponseYou've already chosen the best response.2for example you are given the height which is 1km (the opposite side of the angle of elevation)

freckles
 one year ago
Best ResponseYou've already chosen the best response.2and you are wanting to find the length that airplane has flown for both (which is the adjacent side )

freckles
 one year ago
Best ResponseYou've already chosen the best response.2opp/adj is the tangent ratio

freckles
 one year ago
Best ResponseYou've already chosen the best response.2once you computer x and B (don't ask why I called them that; I wasn't thinking too much about the letters to use) \[\text{ the speed over that 10 sec change }=\frac{\text{ distance traveled in that 10 sec }}{ 10 \sec} \\ \frac{xB}{10 \sec}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thanks. I will manage the rest...

freckles
 one year ago
Best ResponseYou've already chosen the best response.2when you are done with that computation your units should by km/sec but if you don't like how small the number is next to those units you can always covert the sec part to either minutes or hours

freckles
 one year ago
Best ResponseYou've already chosen the best response.2oh your question says to put it an hours

freckles
 one year ago
Best ResponseYou've already chosen the best response.2just let me know if you need any further help with this one

freckles
 one year ago
Best ResponseYou've already chosen the best response.2or if you want me to check your answer
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