BRILLIAthon Day 3 3 , Problem 1 1 of 2 2 , Version 2 2

Geometry Level 1

tan ( x ) 0. 2 r \tan(x) \approx 0.2^{r}

Find x x .


The answer is 0.197731497.

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2 solutions

David Vreken
Jul 25, 2020

Graphing y = tan x y = \tan x and y = 0.2 y = 0.2 and finding the intersection for 0 < x < π 0 < x < \pi gives an x x -value of x 0.197 x \approx \boxed{0.197} .

LaTeX: 20 20

Intelligible Solution: 10 10

Uniqueness: 10 10

Algorithmic Structure: 3 3

Pics: 1 1

Animations: 0 0

Total: 44 44

Awarded 'BRILLIAthon Star' for Problem 5 5

Yajat Shamji - 10 months, 3 weeks ago

tan ( x ) 0.2 x tan 1 ( 0.2 ) x 0.19739 x 0.2 \begin{aligned} \tan (x) &\approx 0.2 \\ x &\approx \tan^{-1} (0.2) \\ x & \approx 0.19739 \\ x &\approx 0.2 \end{aligned}

(This is all true assuming we were calculating in radians)

Do you want me to give you the scores, or not?

Yajat Shamji - 10 months, 3 weeks ago

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Nah, not really, I just posted a solution as it is a normal problem now

A Former Brilliant Member - 10 months, 3 weeks ago

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Do you want to see it though, if you participated?

Yajat Shamji - 10 months, 3 weeks ago

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@Yajat Shamji Fine, if you're so obsessed with it..........

A Former Brilliant Member - 10 months, 3 weeks ago

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@A Former Brilliant Member LaTeX: 20 20

Intelligible Solution: 10 10

Uniqueness: 10 10

Algorithmic Structure: 3 3

Pics: 0 0

Animations: 0 0

Total: 43 43

You would've been awarded 'BRILLIAthon Star' for Problem 5 5 and your total points would've been 111 + 43 = 154 111 + 43 = 154 , 10 10 points behind @David Vreken .

Yajat Shamji - 10 months, 3 weeks ago

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@Yajat Shamji Sleep was still better than this :)

A Former Brilliant Member - 10 months, 3 weeks ago

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@A Former Brilliant Member True, but you would've got 2 2 nd place and got the chance to shape one of my problems and post a problem for me to attempt...

Yajat Shamji - 10 months, 3 weeks ago

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@Yajat Shamji Meh, still sleep

A Former Brilliant Member - 10 months, 3 weeks ago

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@A Former Brilliant Member Can't argue with that - I have insomnia (self-daignosis)...

Yajat Shamji - 10 months, 3 weeks ago

Just remove that ° \degree symbol, because tangent function gives pure numbers as output. @Yajat Shamji

Zakir Husain - 10 months, 3 weeks ago

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@Percy Jackson wanted clarification as he was unsure whether it was degrees or radians, so I said degrees and he requested me to put the degrees symbol up, which I did.

Yajat Shamji - 10 months, 3 weeks ago

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@Yajat Shamji Write it tan ( x ) 0.2 \tan(x)\approx 0.2 as tan \tan function takes angle as input not give it as output

Zakir Husain - 10 months, 3 weeks ago

@Zakir Husain - atan of 0.2 degrees = 1.99999188 degrees, while atan of 0.2 radians = 0.197731497 radians, so there is a difference, and clarity is required :)

A Former Brilliant Member - 10 months, 3 weeks ago

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@A Former Brilliant Member I have changed it to radians...

Yajat Shamji - 10 months, 3 weeks ago

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@Yajat Shamji Radians is not given in superscript, just written normally @Yajat Shamji

A Former Brilliant Member - 10 months, 3 weeks ago

@A Former Brilliant Member What I'm saying is this- tan \tan function gives pure numbers as output for example :

We say that tan ( 30 ° ) = 0.5 \tan(30\degree)=\red{0.5} , 0.5 0.5 is a pure number you can't write it like this tan ( 30 ° ) = 0.5 ° \red{\tan(30\degree)=0.5\red{\degree}} or tan ( 30 ° ) = 0.5 r a d \red{\tan(30\degree)=0.5\red{rad}}

You have to write tan ( x ) 0.2 \tan(x)\approx 0.2 nothing more is required.

Zakir Husain - 10 months, 3 weeks ago

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