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

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

satellite73Best ResponseYou've already chosen the best response.0
i don't think this that easy take a look at the solutions http://www.wolframalpha.com/input/?i=cos%286x%29%3Dsin%283x9%29
 one year ago

RobZBHayesBest ResponseYou've already chosen the best response.0
I'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.
 one year ago

ZeHanzBest ResponseYou've already chosen the best response.1
You 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 \[\sin x =\cos(\frac{ \pi }{ 2 }x)\]
 one year ago

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

RobZBHayesBest 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)
 one year ago

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

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

RobZBHayesBest 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)?
 one year ago

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

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

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

RobZBHayesBest ResponseYou've already chosen the best response.0
I 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
 one year ago

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

RobZBHayesBest ResponseYou've already chosen the best response.0
x=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.
 one year ago

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

HeroBest ResponseYou've already chosen the best response.1
I 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
 one year ago

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

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

HeroBest ResponseYou've already chosen the best response.1
pi = 180 because the length of pi is a semicircle having a measure of 180 degrees.
 one year ago

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

ZeHanzBest ResponseYou've already chosen the best response.1
I 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
 one year ago

RobZBHayesBest ResponseYou've already chosen the best response.0
So 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?
 one year ago

ZeHanzBest ResponseYou've already chosen the best response.1
Yes, 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...
 one year ago

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

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

HeroBest ResponseYou've already chosen the best response.1
If 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.
 one year ago

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

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

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

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

HeroBest ResponseYou've already chosen the best response.1
The equation in that form is the definition of a cofunction. That's how you know.
 one year ago

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

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

HeroBest ResponseYou've already chosen the best response.1
sin(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.
 one year ago

ZeHanzBest 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" ;)
 one year ago
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