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 2 years ago
How do you convert sin into cos, and vice versa.
Promblem: cos(6x) = sin(3x9)
 2 years ago
How do you convert sin into cos, and vice versa. Promblem: cos(6x) = sin(3x9)

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svaibhavi
 2 years ago
Best ResponseYou've already chosen the best response.1cos(6x)= sin(906x)= sin(3x9) sin values are equal u can equate the angles 906x=3x9 99=9x x=11

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0i don't think this that easy take a look at the solutions http://www.wolframalpha.com/input/?i=cos%286x%29%3Dsin%283x9%29

RobZBHayes
 2 years ago
Best ResponseYou've already chosen the best response.0I'm not sure if it's with radians or not but I'm in trig if that helps any. I'm just looking for a conversation rate if there is one.

ZeHanz
 2 years ago
Best ResponseYou've already chosen the best response.1You want to convert to an equation of the form cos a = cos b or sin a = sin b, because these kind of equations have standard solutions:\[\cos a=\cos b \Leftrightarrow a= \pm b+2k \pi\]\[\sin a = \sin b \Leftrightarrow a=b+2k \pi \vee a=\pib+2k \pi\](assuming radians) To get to one of these forms, you can use the following conversions:\[\cos x=\sin(\frac{ \pi }{ 2 }x)\]or \[\sin x =\cos(\frac{ \pi }{ 2 }x)\]

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1x = 11 sin(66) = sin(24) in degrees

RobZBHayes
 2 years ago
Best ResponseYou've already chosen the best response.0@ZeHanz So you're saying I would take cos(6x) and subtract 6x from pi/2 giving me sin(pi/2  6x) being equal to cos(6x)

RobZBHayes
 2 years ago
Best ResponseYou've already chosen the best response.0@Hero I appreciate the answer but I'm looking for an explanation

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1sin(x) = cos(y) are cofunctions, meaning angles x and y are complementary.

RobZBHayes
 2 years ago
Best ResponseYou've already chosen the best response.0@ZeHanz alright so sin(pi/2  6x) = sin(3x9) and cos(6x) = sin(3x9) are the same problem, correct? So how would I go about solving sin(pi/2  6x) = sin(3x9)?

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1You mean it is the same type of problem, right?

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1But not the same exact problem.

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1For sin(pi/2  6x) = sin(3x  9) the angles are equal so pi/2  6x = 3x  9

RobZBHayes
 2 years ago
Best ResponseYou've already chosen the best response.0I tried that and came up with an answer that isn't in my answer choices. I got 0.67453292519943295769236907684886, I'm not sure if it's correct or not though. First I added 6x to both sides giving me pi/2=9x2, then I multiplied everything by 2 giving me pi=18x9, after that I added 9 to both sides leaving me with 12.14159265358979323846264338328=18x, finally I divided everything by 18 giving me x=0.67453292519943295769236907684886. Did I do all of that correctly? @Hero @ZeHanz

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1What are your answer choices?

RobZBHayes
 2 years ago
Best ResponseYou've already chosen the best response.0x=10 x=10 x=11 x=12 You said before that the answer is 11 and I think that's right but I'm trying to get the relation between sin, cos, and tan in case I come across another problem like this one.

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1pi/2  6x = 3x  9 180/2  6x = 3x  9 90 + 9 = 6x + 3x 99 = 9x 99/9 = x 11 = x

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1I already explained to you the relationship sin(x) = cos(y) if x and y are complementary tan(x) = cot(y) if x and y are complementary csc(x) = sec(y) if x and y are complementary

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1Those are properties of cofunctions

RobZBHayes
 2 years ago
Best ResponseYou've already chosen the best response.0So the covertion of sin to cos and vice versa is always pi/2x and pi always equals 180?

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1pi = 180 because the length of pi is a semicircle having a measure of 180 degrees.

RobZBHayes
 2 years ago
Best ResponseYou've already chosen the best response.0Oh ok, I wasn't aware that pi was a semicircle lol. I guess that's kind of sad considering I'm in trig _

ZeHanz
 2 years ago
Best ResponseYou've already chosen the best response.1I guess "being in trig" means you have to do everything in degrees and do not need to worry about angles greater than 180 degrees (or 360?) and smaller than 0? In that case I would solve the equation as follows:\[\cos 6x=\sin (3x9) \Leftrightarrow \cos 6x=\cos(90  (3x9))=\cos((993x)\]This would give:\[6x=\pm (993x)\]which means\[6x=993x \vee 6x=3x99 \Leftrightarrow\]\[9x=99 \vee 3x=99 \Leftrightarrow x=11 \vee x=33\]So x=11 would be the only answer that is left, so option C

RobZBHayes
 2 years ago
Best ResponseYou've already chosen the best response.0So if I want to solve cos(2x4)=sin(6x) the first thing I would want to do is convert sin(6x) into a cos, and that would be cos(pi/26x). Then my equation would be 2x4=pi/26x, so if I were to simplify that It would be 2x4=906x, then I would want to subtract 2x from both sides giving me 4=908x, then I would subtract 90 from both sides giving me 94=8x, finally I would want to divide everything by 8x giving me my final answer as x=11.75 as a final answer, right?

ZeHanz
 2 years ago
Best ResponseYou've already chosen the best response.1Yes, but there is no need to use radians first and then degrees. If you do this, you make things much more difficult for yourself.Either do everything in degrees, or do evertything in radians. Further, I'm still unsure about what "being in trig" means. I would get:\[2x4= \pm 906x\]so\[2x4=906x \vee 2x4=6x90 \Leftrightarrow\]\[8x=94 \vee 4x=86 \Leftrightarrow\]\[x=11.75 \vee x=21.5\]The last solution coming from the negative solution, which can probably be discarded...

RobZBHayes
 2 years ago
Best ResponseYou've already chosen the best response.0Trig is a shortened way of saying Trigonometry

ZeHanz
 2 years ago
Best ResponseYou've already chosen the best response.1Which means every angle is an angle in a triangle?

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1If you wanted to solve cos(2x4)=sin(6x) knowing that angles 2x  4 and 6x are complementary you would simply add both equations together and set them equal to 90 2x  4 + 6x = 90 8x  4 = 90 8x = 94 x = 94/8 x = 11.75 in degrees.

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1@ZeHanz, your approach seems to include unnecessary steps.

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1All one needs to know is that if sin(x) = cos(y) then you are dealing with cofunctions where x and y are complementary.

RobZBHayes
 2 years ago
Best ResponseYou've already chosen the best response.0Our of curiosity how would you determine if the angles are in fact complementary in these types of equations?

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1If you see a situation where you have an equation of the form sin(x) = cos(y), then x and y must be complementary.

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1The equation in that form is the definition of a cofunction. That's how you know.

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1It's not the mystery you're making it out to be. Cofunctions are simply a property of trigonometric functions

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1http://www.barstow.edu/lrc/tutorserv/handouts/045%20Trigonometric%20Properties.pdf

Hero
 2 years ago
Best ResponseYou've already chosen the best response.1sin(x) = cos(y) is a general form of a cofunction identity where x and y are complementary angles such that x + y = 90 sin(6x) = cos(2x  4) is a specific form of the cofunction identity where solving 6x + (2x  4) = 90 for x reveals the complementary angles.

ZeHanz
 2 years ago
Best ResponseYou've already chosen the best response.1@Hero: I understand now these equations are not about the sin and cos functions defined for every real number, but that they are connected to sin and cos as defined in triangles. That explains my "unnecessary steps" ;)
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