Working with Arctan

[Jason76]

How can I get an \(\displaystyle \arctan\) situation out this equation?

\(\displaystyle 0 = 5\tan\dfrac{x}{6}\)

Here is my attempt (correct me if algebra is wrong):

\(\displaystyle 0 = 5\tan\dfrac{x}{6}\)

\(\displaystyle (\dfrac{1}{5}) 0= (\dfrac{1}{5})5\tan\dfrac{x}{6}\)

\(\displaystyle 0 = \tan\dfrac{x}{6}\)

\(\displaystyle (6)0 = \tan\dfrac{x}{6}(6)\)

\(\displaystyle 0 = \tan x\)

\(\displaystyle \arctan(0) = 0\)

 

[MarkFL]

You should note that in general:

\(\displaystyle k\tan(\theta)\ne\tan(k\theta)\)

 

[mmm4444bot]

\(\displaystyle 0 = \tan\dfrac{x}{6}\)

\(\displaystyle (6)0 = \tan\dfrac{x}{6}(6)\)

x/6 is the input to the tangent function. You may not cancel the 6 in the denominator of the input via multiplying both sides of that equation by 6 because the Order of Operations tells us to evaluate the tangent of x/6 before doing anything else.

In other words, the expression tan(x/6) is not the same as tan(x)/6.

tan(x/6) is the tangent of the angle x/6 radians

tan(x)/6 is one-sixth the tangent of x radians

You've made this same mistake with function notation before. Do you need help understanding?

 

[mmm4444bot]

How can I get an \(\displaystyle \arctan\) situation

out this equation?

\(\displaystyle 0 = 5\tan\dfrac{x}{6}\)

What is your definition of "an arctan situation"?

Are you trying to ask how to solve the equation using the arctangent function?

If so, then after you get to 0 = tan(x/6), take the arctangent of each side:

arctan(0) = arctan[tan(x/6)]

0 = x/6

Now you may multiply both sides by 6, to solve for x.

 

[Jason76]

What is your definition of "an arctan situation"?

Are you trying to ask how to solve the equation using the arctangent function?

If so, then after you get to 0 = tan(x/6), take the arctangent of each side:

arctan(0) = arctan[tan(x/6)]

0 = x/6

Now you may multiply both sides by 6, to solve for x.

Thanks, big mistake by not taking both sides. I will update all my posts in the next day or so with this new info.

 

[Deleted member 4993]

To avoid this confusion, I always write sin(x) or tan(x/6), even sin(Θ) where the chance of confusion is less. Isn't it ironic that Khan is trying to avoid KHAN_fusion!!

 

[Deleted member 4993]

How can I get an \(\displaystyle \arctan\) situation out this equation?

\(\displaystyle 0 = 5\tan\dfrac{x}{6}\)..........If your problem is stated way, it means → 0 = 5 * tan(x/6) and NOT0 = 5 * (1/6) * tan(x)

,

 

[Jason76]

I will try to update my posts in the next day or so with a more clear syntax. One that shows I'm taking the \(\displaystyle \tan\) OF some number by using parenthesis around the number.

 

[mmm4444bot]

I will try to update my posts in the next day or so with a more clear syntax. One that shows I'm taking the \(\displaystyle \tan\) OF some number by using parenthesis around the number.

Please consider adopting the syntax that mathematicians use.

It's called "function notation", and you may read about it starting HERE. :cool: