Maths question, need help!

[titaniumx3]

A little stuck with the following trigonometry question, would appreciate some help!

Solve cot(2x)-tan(78)=1/2*sec(x)*sec(78) for 0<=x<=360 degrees.

I've gotten it to cos(2x+78)=sin(x) but not sure what to do now or if this is completely wrong.

Would really appreciate some help!

 

[muon]

https://www.wolframalpha.com/input/?i=cot(2x)-tan(78)=1/2*sec(x)*sec(78)

The exact forms look ridiculous.

 

[bainbridge]

I don't know why I clicked on this thread because I'm useless at anything other than simple arithmetic.

 

[Impy77]

sin(x)=cos(90-x) basic trig id
implies 2x-78=90-x from your equation.
then solve for x
this all assumes your rearrangement is correct....i cant be botherdd to check that

 

[Mr Jack]

https://www.wolframalpha.com/input/?i=cot(2x)-tan(78)=1/2*sec(x)*sec(78)

The exact forms look ridiculous.

Your units are wrong, Wolfram uses sensible radians but the question is asked in degrees.

 

[muon]

Your units are wrong, Wolfram uses sensible radians but the question is asked in degrees.

Had a feeling it might be that. Just couldn't be bothered to find the degrees character symbol.

https://www.wolframalpha.com/input/?i=cot(2x)-tan(78°)=1/2*sec(x)*sec(78°)

 

[titaniumx3]

sin(x)=cos(90-x) basic trig id
implies 2x-78=90-x from your equation.
then solve for x
this all assumes your rearrangement is correct....i cant be botherdd to check that

I did this and got one solution, but how do you get the rest of them? Plotting the two graphs shows four solutions within the required range.

 

[nine_tails]

42

 

[ps3ud0]

I did this and got one solution, but how do you get the rest of them? Plotting the two graphs shows four solutions within the required range.

Then your simplification must be wrong as that only leads to a single solution as per Impy77s answer

ps3ud0

 

[Mr Jack]

Then your simplification must be wrong as that only leads to a single solution as per Impy77s answer

No. Because Sin and Cos are periodic, there are an infinite number of solutions to sin(y) = cos(x), our OP needs to work out all the ones in the range 0-360

 

[Borealis]

No. Because Sin and Cos are periodic, there are an infinite number of solutions to sin(y) = cos(x), our OP needs to work out all the ones in the range 0-360

This.

Doesn't help that the question is in degrees. For this sort of stuff, radians are so much easier to work with.