Ive been given a question and I know the answer but I just cant figure out how a certain value is achieved..?

Question:
Find the solution to tan(3x) = 0.65 given that x lies between 5pi/3 and 2pi ..

In the answer it says "Given 3x = .576 then tan(3x) = 0.65"

It looks simple but I just dont know how they've got .576? How is it given?

 

\( tan (3x) = 0.65 \)

\( 3x = Arctan (0.65) \)

\( 3x \approx 0.576 \)

\( Arctan = tan^{-1} \)

I would just like to point out .576 is in radians by the way not degrees.

 

Oh my gosh I'm so ditzy.. Just realized it's in radians.. I looked at your input and it made sense haha thankyou!!

Arctan(0.65 = 33.024 Degrees
33.024/(180/pi) = 0.576 Radians

 

As a sidenote try and get into the habit of always working with radians as much as possible.

Only express an answer in degrees if you're asked to do so.

 

Also get in the habit of always indicating your units -- all the way through your work, not just tacked on as an afterthought at the end.

 

Thankyou both for your input, it's very helpful. It's worth 10% on a unit and I'm getting 92% overall its just one last question if you will please.. For the extra 8% ..

The worked solution of this question is easy up until it states: 'a' to be 0.927295? How is this result achieved?

 

Also get in the habit of always indicating your units -- all the way through your work, not just tacked on as an afterthought at the end.

I'll hold my hands up to that. Yes I did forget to indicate the unit for radians from which is why I "tacked" it on as an "afterthought" so as to prevent Ben C form scratching his head not realising that his calculator was is in degree mode.

Ben C you can use a small "c" as a subscript to indicate "circular measure." In other words, radians.

\( 0.576^{c} \)

 

Yes I understand that I'm sure after many more posts I'll get the hand of implementing them in the correct way
If you could help with my last question I would appreciate it massively my deeadline's in 2 hours and I really want 100% on this topic

 

Post #2 will give you a clue.

 

I've done it now thanks for all your input

(ArcCos(6/10))/(180/pi) = 0.927295

 

\( 0.927295^{c} \)

 

I'll hold my hands up to that. Yes I did forget to indicate the unit for radians from which is why I "tacked" it on as an "afterthought" so as to prevent Ben C form scratching his head not realising that his calculator was is in degree mode.

Ben C you can use a small "c" as a subscript to indicate "circular measure." In other words, radians.

\( 0.576^{c} \)

I actually wasn't referring to your post at all, but just making a blanket general statement.

'radians' are a dimensionless unit (length/length) so it's hard to say that it is 'wrong' if they are left off. Provided you never leave of degrees or grads or whatever other unit of measure you might express it in, then you quickly develop the habit of thinking of any angle that does not have units as being radians. But I definitely prefer to carry 'radians' but I also drop in when it would no longer add clarity to the expression and add it when having it would add clarity.