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3 years ago

Jason has 4 tiles. each tile has a number printed on it. the numbers are 2, 6, 8.

Mathematics

1 answer:

bearhunter [10]3 years ago

5 0

Hi Im Carriyana!! Glad to help today!

If jason has 4 tiles and...

tile #1 says 2

tile #3 says 6

tile #4 says 8

Simple math states that tile #2 is 4!!

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$\bold{cot(t) =\dfrac{12}{5}}$

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That means, angle $t$ is in the 3rd quadrant.

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Value of cot(t)

Solution:

First of all, let us recall what trigonometric ratios are positive and what trigonometric ratios are negative in 3rd quadrant.

In 3rd quadrant, tangent and cotangent are positive.

All other trigonometric ratios are negative.

Let us have a look at the following identity:

$cosec^2\theta -cot^2\theta =1$

here, $\theta =t$

So, $cosec^2t-cot^2t=1$

$\Rightarrow (-\dfrac{13}{5})^2-cot^2t=1\\\Rightarrow (\dfrac{169}{25})-cot^2t=1\\\Rightarrow \dfrac{169}{25}-1=cot^2t\\\Rightarrow \dfrac{169-25}{25}=cot^2t\\\Rightarrow \dfrac{144}{25}=cot^2t\\\Rightarrow cot(t)=\pm\sqrt{\dfrac{144}{25}}\\\Rightarrow cot(t)=\pm\dfrac{12}{5}$

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$\bold{cot(t) =\dfrac{12}{5}}$

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