# Inverse trig question (1 Viewer)

#### idkkdi

##### Well-Known Member
Daily struggles of a 4U kid....
i would bet this stuff was allowed in the 20th century where HSC maths was better lol.

#### Trebla

ur trolling.
inverse sin + inverse cos = pi/2 is like by definition basically.
is this assuming?
No, I’m talking about your inverse cosine result that you called on.

#### idkkdi

##### Well-Known Member
No, I’m talking about your inverse cosine result that you called on.
if x+y =z
and there's an equation
x+3a = z
obviously 3a = y no?

#### Qeru

##### Well-Known Member
if x+y =z
and there's an equation
x+3a = z
obviously 3a = y no?
If it took you three lines to explain that it isn't so obvious?

#### idkkdi

##### Well-Known Member
If it took you three lines to explain that it isn't so obvious?
.....
x + 3a = z
3a = y (from an identity that is obvious)
----------------------> this was my working in solution lol.
so two lines.

#### idkkdi

##### Well-Known Member
If it took you three lines to explain that it isn't so obvious?
i love how we're considering these parts.
the last lines of my solution are even less obvious hahahaha. honestly not bothered to latex or type reasoning.
have fun looking at it lol.

#### idkkdi

##### Well-Known Member
If it took you three lines to explain that it isn't so obvious?
On the subject of unobvious-ity. i doubt i would see that hidden quadratic you did in suitable minutes in an exam.

#### Trebla

I think the use of the word “obviously” was misleading because normally that is used to call on a result, not used in place of a “hence” or “therefore”.

Either way, the part where you have an equation in terms of u is not trivial and is missing some working.

#### Trebla

On the subject of unobvious-ity. i doubt i would see that hidden quadratic you did in suitable minutes in an exam.
Actually, the part where you had
$\bg_white 2\cos^{-1} (x) = \cos^{-1} (3x+1)$
lends itself to an obvious quadratic by cosine double angles.

#### idkkdi

##### Well-Known Member
I think the use of the word “obviously” was misleading because normally that is used to call on a result, not used in place of a “hence” or “therefore”.

Either way, the part where you have an equation in terms of u is not trivial and is missing some working.
we all know mathematicians use 'trivial' to skip working out because they're a tad lazy hahaha.

#### idkkdi

##### Well-Known Member
Actually, the part where you had
$\bg_white 2\cos^{-1} (x) = \cos^{-1} (3x+1)$
lends itself to an obvious quadratic by cosine double angles.
???????

#### Trebla

we all know mathematicians use 'trivial' to skip working out because they're a tad lazy hahaha.
Yeah, once you become an actual mathematician and writing academic papers. That will never fly in an exam at school or uni though lol

#### idkkdi

##### Well-Known Member
oh ye pretty nice quadratic. working out up to that quadratic looks nicer than @Qeru's lol.

#### idkkdi

##### Well-Known Member
Yeah, once you become an actual mathematician and writing academic papers. That will never fly in an exam at school or uni lol
but it flies in textbooks lol.
Though trivial is a toned down version of the true mathematician phrase when writing textbooks,
"the proof(/example) is left as an exercise to the reader"

#### Qeru

##### Well-Known Member
I think if you explained why $\bg_white \sin^{-1}(x)+\cos^{-1}(x)=\frac{\pi}{2}$ and added some explanation between steps your proof would have made more sense.

#### idkkdi

##### Well-Known Member
I think if you explained why $\bg_white \sin^{-1}(x)+\cos^{-1}(x)=\frac{\pi}{2}$ and added some explanation between steps your proof would have made more sense.
dont u learn that in junior years?

#### Qeru

##### Well-Known Member
You could have done $\bg_white \sin(\theta)=\cos\left(\frac{\pi}{2}-\theta\right)$ where $\bg_white \theta=\sin^{-1}(x)$ which is a basic definition that is allowed, to prove the inverse formula. Also like Trebla said you could do $\bg_white \cos(2\cos^{-1}(x))=3x+1 \implies 2x^2-1=3x+1$ I think this is a more logical progression.

#### Etho_x

##### Well-Known Member
This must be what it’s like when mathematicians have fights :0 “No this is trivial!” “No you’re trivial stfu” or things along the lines of that I’d guess