- Confusionist

Can someone help me solve this?
cos(x^2+45)+tan(4x+90) = sin(3x+120)
A step by step would be great.

- katieb

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- anonymous

by solving do you mean proving?

- Confusionist

Yes. :)

- myininaya

What methods have been discussed?

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## More answers

- myininaya

We are solving for x not proving this. This isn't an identity.

- myininaya

Or does it say to disprove or prove?

- Confusionist

Ah yes, my bad. It says solve.

- myininaya

Can you tell me what methods in class have been discussed?

- Confusionist

None, this is from a book with only problems I picked up at barnes and noble. We haven't done this and wont do it for another year or two. I've had no problems with the book up to this point.

- myininaya

can you tell me what methods the book has discussed?

- Confusionist

None. It's a book of only problems. It starts from Geometry and works it's way up in problems.

- myininaya

Name of book please

- Confusionist

Math Review for the High School Classroom

- Confusionist

I looked for it online and can't find it.

- myininaya

I didn't see the book. :(
So there are no examples?

- Confusionist

No examples, just questions. :c How did you learn it?

- myininaya

Honestly, I don't know without seeing some example or them mentioning some method they want to use.

- Confusionist

Ah, okay. Thanks, anyway. :)

- shamil98

cos(x^2+45)+tan(4x+90) = sin(3x+120)
cos(x^2+45)+sin/cos(4x+90) = sin(3x+120)
dividing everything by sin.
tan(x^2+45) + sec(4x+90) = 3x + 120
i don't remember trig that well, but you can convert it to this i think.

- myininaya

You can't do that...
Like you can't divide by the trig part
The trig part is a function not a number or variable on its own

- shamil98

oh

- primeralph

Are the angles in radians or degrees?

- primeralph

I'll assume degrees for now.

- Confusionist

Degrees, yeah. ^^

- hartnn

45,90,120 suggest they are in degrees...
we can convert sin and cos in tan,
like cos A = tan (sqrt (1-A^2)/A)
something like this
and then use tan A+tan B formula......
but if thats possible, the algebra is going to be very ugly....

- myininaya

but @hartnn tan(90) does not exist
you were talking about the sum identity for tan right?

- primeralph

@myininaya tan(a+90) = -1/tan(a), since they're perpendicular.

- hartnn

not tan(A+B)
tan A +tan B , where B = 4x+90
and yeah, tan (A+90) = - cot 90
so maybe convert cos into cot and use cotA-cotB formula...
i don't think that will be of any use though....

- primeralph

|dw:1388481204906:dw|

- myininaya

I don't like the x squared part much.

- primeralph

Series solution is what I'd prefer to us,e but not without an attempt with standard algera.

- myininaya

or maybe the whole problem
i don't see how to do it with algebra/trig
He said it was for high school though

- hartnn

even wolf doesn't give integral or rational solutions...

- Confusionist

Yes, I'm a junior in high school, but the book said High School. It extends way past what I expect to learn in High School, though. I think they may have the age range a bit messed up.

- primeralph

No simple way to solve at that level.

- myininaya

@primeralph if you want, can you show me your series thing you were talking about?
You know if you want to.

- Confusionist

I might just go and ask one of the professors at the college I intern at. Thanks for your help, guys. :)

- primeralph

First I'd have to convert all to radians.

- primeralph

Then find a way to represent the equation as a DE, or simply use the Taylor power series.

- myininaya

what is equivalent to a (1 radian) squared?
That bugs me. The little square there.

- myininaya

What I'm saying is I'm not used to looking at angles being squared

- primeralph

|dw:1388481895287:dw|

- primeralph

@myininaya Yeah I understand, but you'd have to extend your thinking beyond expecting trig to only apply to angles.

- primeralph

It will be extensive, but in the end, there might be real solutions.

- myininaya

x^2 and 45 will have different units

- myininaya

we have x^2=a^2 (degs)^2
and 45 is just in degs not degs^2

- primeralph

The x^2 term will be set to have some correction factor.
After taking a look at it, I think it's solvable algebraically. It's just long.

- primeralph

And with a lot of restrictions to be imposed.

- hartnn

those ugly solutions
http://www.wolframalpha.com/input/?i=cos%28x%5E2%2B45%29%2Btan%284x%2B90%29+%3D+sin%283x%2B120%29&dataset=

- primeralph

Don't think you used radians. Wolfram is radians by default.

- hartnn

doesn't make much difference
http://www.wolframalpha.com/input/?i=cos%28x%5E2%2Bpi%2F4%29%2Btan%284x%2Bpi%2F2%29+%3D+sin%283x%2B2pi%2F3%29

- myininaya

wolfram doesn't want to solve it
this is the way input it
cos((x deg)^2+45 deg)+tan(4x deg+90 deg)=sin(3x deg+120 deg)
http://www.wolframalpha.com/input/?i=cos%28%28x+deg%29%5E2%2B45+deg%29%2Btan%284x+deg%2B90+deg%29%3Dsin%283x+deg%2B120+deg%29

- myininaya

Maybe it doesn't like the unlike units being added either
idk

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