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

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svaibhavi
 one year 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
 one year 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
 one year 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
 one year 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
 one year ago
Best ResponseYou've already chosen the best response.1x = 11 sin(66) = sin(24) in degrees

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

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

RobZBHayes
 one year 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
 one year ago
Best ResponseYou've already chosen the best response.1You mean it is the same type of problem, right?

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

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

RobZBHayes
 one year 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
 one year 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
 one year 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
 one year ago
Best ResponseYou've already chosen the best response.1Those are properties of cofunctions

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

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

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

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

Hero
 one year 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
 one year 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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