July 5th, 2017, 01:05 AM  #1 
Newbie Joined: Jul 2017 From: Somewhere Posts: 13 Thanks: 0  Basic questions
Recently, I have just learnt a bit about the basics of trigonometry and have some questions about it. Such as why is it when 2cos(θ)=√2, it will be cos$^{1}$(√2 /2) Thanks. Last edited by skipjack; July 6th, 2017 at 05:49 AM. 
July 5th, 2017, 01:32 AM  #2 
Math Team Joined: Jul 2013 From: काठमाडौं, नेपाल Posts: 442 Thanks: 36 Math Focus: Elementary Mathematics 
Do you mean, $\displaystyle θ = \arccos{(\sqrt {2}/2)}$ 
July 5th, 2017, 01:53 AM  #3 
Newbie Joined: Jul 2017 From: Somewhere Posts: 13 Thanks: 0 
I haven't learnt the meaning of arccos yet:/

July 5th, 2017, 02:02 AM  #4 
Math Team Joined: Jul 2011 From: Texas Posts: 2,569 Thanks: 1272 
$2\cos{\theta}=\sqrt{2} \implies \cos{\theta}=\dfrac{\sqrt{2}}{2}$ Determining $\theta$ requires use of the inverse cosine function. In other words, if $\cos{x}=y$, then $x=\cos^{1}{y}$, also written $x=\arccos{y}$ $\theta = \cos^{1}\left(\dfrac{\sqrt{2}}{2}\right) = \dfrac{\pi}{4}$ because $\cos\left(\dfrac{\pi}{4}\right) = \dfrac{\sqrt{2}}{2}$ Go to the link for a very basic explanation of inverse trig functions ... https://www.khanacademy.org/math/geo...unctionsintro 
July 5th, 2017, 04:16 AM  #5 
Newbie Joined: Jul 2017 From: Somewhere Posts: 13 Thanks: 0 
But is it possible for the tangent to cross out/remove the other tangents? Or must it be tan(63) divided by tan(34)? etc. tan(34)=tan(63) Last edited by skipjack; July 6th, 2017 at 05:50 AM. 
July 5th, 2017, 05:23 AM  #6  
Math Team Joined: Jul 2011 From: Texas Posts: 2,569 Thanks: 1272  Quote:
fyi, $\tan(34) \ne \tan(63)$ Last edited by skipjack; July 6th, 2017 at 05:50 AM.  
July 5th, 2017, 05:33 AM  #7 
Newbie Joined: Jul 2017 From: Somewhere Posts: 13 Thanks: 0 
Just a small question out of curiosity, sorry :c
Last edited by skipjack; July 6th, 2017 at 05:51 AM. 
July 5th, 2017, 05:42 AM  #8 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,225 Thanks: 420 Math Focus: Yet to find out.  Not a problem to ask other questions, but it's important to be as clear as you can, even if you don't fully understand the topic (or even what you're asking!). So, what is it about the tangent function that has you stuck? Last edited by skipjack; July 6th, 2017 at 05:51 AM. 
July 5th, 2017, 05:54 AM  #9 
Newbie Joined: Jul 2017 From: Somewhere Posts: 13 Thanks: 0 
Well, is there a simplified explanation as to why sin will change to sin$^{1}$ when we are counting ratio and angles? And with regards to the previous question, can a tangent cross out another tangent? Like are they both of same value? Or must we calculate the output value before dividing, such as tan(63)/tan(34) 3tan(34) = tan(63) I'm extremely sorry for this question that definitely has a lack of clarity;I'm not good at expressing things out. Last edited by skipjack; July 6th, 2017 at 05:46 AM. 
July 5th, 2017, 05:55 AM  #10 
Senior Member Joined: Jun 2015 From: England Posts: 624 Thanks: 170 
To answer your question Tangents, sines and cosines are just numbers. They are generally different numbers for different angles. So you cannot cancel a tangent, sine or cosine on one side of an equation with a tangent, sine or cosine on the other side of an equation unless they refer to the same angle. I also have some sketches for you on the other site I have yet to upload. 

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