Trigonometry question

[shakirmoledina]

Hey guys,

last time I had asked a question which Veho had answered instantaneously.

If possible help me prove the following

cossec2x = secx + cotx

Please prove from both sides

 

[trumpet-205]

Is it csc 2x or (csc x)^2?

 

[shakirmoledina]

let me confirm that cuz even it doesnt seem to match when putting values in there

 

[calmwaters]

cossec2x - secx = cotx

In other words, you can divide everything by x and end up with

cossec2 - sec = cot
factor out the sec and get this

sec(cos2 - 1) = cot

sec((cos*2) - 1) = cot

help much?

Edit: And I guess x stands for the degree, right?

(where this symbol >> ^ << stands for the degree symbol)
sec 90^ ((cos 90^) * 2) - 1) = cot 90^

 

[trumpet-205]

In other words, you can divide everything by x and end up with

In trig, you cannot just divide variable. Trig works very differently than Algebra.

And unless specified, by default trig uses radiant, not degree or gradiant.

 

[calmwaters]

In trig, you cannot just divide variable. Trig works very differently than Algebra.

And unless specified, by default trig uses radiant, not degree or gradiant.

Never the less, it's still a mathematical equation. In this case, it's taking the cosecant of the angle multiplied by two and setting it equal to the secant plus the cotangent.
So let's say the angle is 45 degrees. The left side would be the cosecant of 90 (since x was multiplied by 2) and that's being set equal to the secant of 90 degrees plus the cotangent of 90 degrees.

Besides, when you're involving secant or sine functions in a mathematical equation, it probably means you're talking about angles. Plus, algebra is used by nearly every other math type there is. They contain variables, which can be used for anything since variables don't have a set value. When they do, they become constants, kind of like the number 14 or 56 degrees.

 

[trumpet-205]

Besides, when you're involving secant or sine functions in a mathematical equation, it probably means you're talking about angles.

Nope. Trig, be it in the context of Algebra or Calculus, is in radiant unless you put a degree notation.

If an equation calls for sin (12), you use radiant. Yon only use degree mode when it is written as sin (12 deg). In math, we operate trig as if we are talking about unit circle. For example, we express 180 deg as pi, and 90 deg as pi/2.

It is sort of like square root. If you don't put negative sign before the square root the answer is positive no matter what (principle of square root).

Example: squ(25) = 5, but -squ(25) = -5.

 

[Fat D]

You cannot prove it because the two sides are not identical in the first place.

 

[calmwaters]

Nope. Trig, be it in the context of Algebra or Calculus, is in radiant unless you put a degree notation.

If an equation calls for sin (12), you use radiant. Yon only use degree mode when it is written as sin (12 deg). In math, we operate trig as if we are talking about unit circle. For example, we express 180 deg as pi, and 90 deg as pi/2.

It is sort of like square root. If you don't put negative sign before the square root the answer is positive no matter what (principle of square root).

Example: squ(25) = 5, but -squ(25) = -5.

If an angle is in radians, then you must put 'rad' after it to specify this. Angles have always been viewed as being 0 to 360 degrees: if an angle is not in degrees, then you must put the appropriate symbol after the number.


If an angle is in radians, you must convert it to degrees before you can take the sine of it; give me the sine of 12 radians. And a gradient is a texture which is created by mixing two or more colors. And the square root example: if you don't put a subtraction symbol before any variable, it's assumed to be positive. If you put a negative symbol before the sine, then you'll be taking the inverse sine of that number. If you put a radian symbol after a number and a subtraction symbol before the number, then you will have

 

[Felipe_9595]

If an angle is in radians, then you must put 'rad' after it to specify this. Angles have always been viewed as being 0 to 360 degrees: if an angle is not in degrees, then you must put the appropriate symbol after the number.


If an angle is in radians, you must convert it to degrees before you can take the sine of it; give me the sine of 12 radians. And a gradient is a texture which is created by mixing two or more colors. And the square root example: if you don't put a subtraction symbol before any variable, it's assumed to be positive. If you put a negative symbol before the sine, then you'll be taking the inverse sine of that number. If you put a radian symbol after a number and a subtraction symbol before the number, then you will have

Dude, i dont wanna be a prick, but you clearly have no idea about what are you talking. Radians is an adimensional unit and its the standard measure in trigonometry. There is a reason why the perimeter of a circunference is 2Pi*r and not 2*360°*r

Also, no ? Take any decent calculator and put sin(90), awnsers will not be 1.

 

[calmwaters]

Dude, i dont wanna be a prick, but you clearly have no idea about what are you talking. Radians is an adimensional unit and its the standard measure in trigonometry. There is a reason why the perimeter of a circunference is 2Pi*r and not 2*360°*r

Also, no ? Take any decent calculator and put sin(90), awnsers will not be 1.

That may be, but the standard measurement when dealing with circles is degrees. (And 2π is 360 degrees)... And even though it is the standard measurement in trigonometry, you should still put 'rad' after it. And if I put the sine of 90 degrees into the calculator, it'll give me one answer and it better be one. Because the cosine of 90 degrees is 0. The circumference of a circle is equal to the degree times the radius. Since 2π is 360 degrees. And 2π/3 is 120 degrees. etc.

But I'd prefer not to answer any more statements since this thread might become locked because of it.

 

[Felipe_9595]

That may be, but the standard measurement when dealing with circles is degrees. (And 2π is 360 degrees)... And even though it is the standard measurement in trigonometry, you should still put 'rad' after it. And if I put the sine of 90 degrees into the calculator, it'll give me one answer and it better be one. Because the cosine of 90 degrees is 0. The circumference of a circle is equal to the degree times the radius. Since 2π is 360 degrees. And 2π/3 is 120 degrees. etc.

But I'd prefer not to answer any more statements since this thread might become locked because of it.

No, please stop being so obsessed, it isnt. Radians its the standard, i havent used degrees in almost four years (basically, high school, when "kids" gets confused about radians >degrees), i am studying engineering and we have NEVER used degrees, only Radians.

 

[Zaide]

Guys... as long as you convert properly between radians and degrees it makes absolutely no difference which you use to solve this identity. Your argument about which is standard has no relevance.

EDIT: Also, as Fat D said, you must have a typo because those two sides are NOT equivalent. Just plug it into a calculator with any value for X and you'll see that both sides do not produce the same value.

 

[shakirmoledina]

The qn is incorrect. argument useless and therefore should be dropped... alongwith this topic. My friend gave me an incorrect question.

 

[Niksy]

That may be, but the standard measurement when dealing with circles is degrees. (And 2π is 360 degrees)... And even though it is the standard measurement in trigonometry, you should still put 'rad' after it. And if I put the sine of 90 degrees into the calculator, it'll give me one answer and it better be one. Because the cosine of 90 degrees is 0. The circumference of a circle is equal to the degree times the radius. Since 2π is 360 degrees. And 2π/3 is 120 degrees. etc.

But I'd prefer not to answer any more statements since this thread might become locked because of it.

Just as others have pointed out - it is accepted that when talking about trigonometry you use radians unless specified otherwise. sin(90) is not the same as sin(90°). Could you please provide info on why you think it is otherwise? Did you study trigonometry in a different way?

 

[evandixon]

All this arguing...
Radians vs Degrees...
Always specify the unit unless a particular class always uses one or the other.
But it's usually safe to assume if no unit is given. Numbers like 90, 180, 30 are usually degrees, and multiples of pi are usually radiant (although I haven't seen pi degrees before).

 

[calmwaters]

Just as others have pointed out - it is accepted that when talking about trigonometry you use radians unless specified otherwise. sin(90) is not the same as sin(90°). Could you please provide info on why you think it is otherwise? Did you study trigonometry in a different way?

Enter sin(90) into your calculator and then enter sin(90°). Then tell me what you get. I've said this before: radians must be converted to numeric degrees before you can take the sine of them. And it is not accepted: that's what your teacher tells you. Your teacher means that you should be able to convert degrees into radians and back again when dealing with a circle or any other geometric shape: get this through your thick skull.

Jeez, I'm getting blasted for solving a mathematical equation by using actual variables instead of writing a long paragraph. I didn't see any of you 'math experts' doing this.

 

[Felipe_9595]

Enter sin(90) into your calculator and then enter sin(90°). Then tell me what you get. I've said this before: radians must be converted to numeric degrees before you can take the sine of them. And it is not accepted: that's what your teacher tells you. Your teacher means that you should be able to convert degrees into radians and back again when dealing with a circle or any other geometric shape: get this through your thick skull.

Jeez, I'm getting blasted for solving a mathematical equation by using actual variables instead of writing a long paragraph. I didn't see any of you 'math experts' doing this.

http://en.wikipedia.org/wiki/Radian

The reason rads. are the standard is because, in calculus, degrees make verything complicated, for example, the taylor series for sin(x) is:

http://upload.wikimedia.org/math/4/8/c/48c5cd3f92a3344fa1ee8e2b429d87a9.png (rads)

while in degrees is:

http://upload.wikimedia.org/math/0/2/0/0201271886336aedeb1480c16f85f1fd.png

Also, its obvious that your mathematical knowledge is null if you end canceling the X's in each side of an equation inside trigonometrical functions.

 

[calmwaters]

The reason rads. are the standard is because, in calculus, degrees make everything complicated, for example, the Taylor series for sin(x) is:

http://upload.wikimedia.org/math/4/8/c/48c5cd3f92a3344fa1ee8e2b429d87a9.png (rads)

while in degrees is:

http://upload.wikimedia.org/math/0/2/0/0201271886336aedeb1480c16f85f1fd.png

Also, its obvious that your mathematical knowledge is null if you end canceling the X's in each side of an equation inside trigonometrical functions.

Well since radians are the standard in calculus, then you've got to be able to convert them from degrees since degrees are used in all the other maths.

Radians are ONLY used as the standard measurement in calculus: everything else, and I do mean everything else, uses degrees as the standard measurement. This is why it's important to be able to seamlessly convert degrees to radians and back again: they're the standard unit of measurement in calculus.

And you think insulting my math abilities will make you look smarter? Think again, dumbass. Once you resort to insulting someone, then it's obvious you're dumber than them since you can't come up with any reasonable solution to the other person's answers. But obviously I've inadvertently hurt your pride, so I'll stop now. So now quit trolling me.

 

[Smuff]

The answer is "7". You are welcome.

PS. I have a masters in applied mathematics from Cambridge, but I'm not getting involved.