Mathematics: Sec 330 find the exact value in simplest form with a rational denominator

The answer would be (2^16.3^6y^6)...

Sec 330 find the exact value in simplest form with

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milkshakegrande101

21.06.2021

Mathematics

$\implies \sec 3 30^o = \dfrac{2}{\sqrt3}=\dfrac{2\sqrt{3}}{3}$

Step-by-step explanation:

Given :-

$\sec 330^o$

And we need to find out its value . Firstly we know that 330° lies in 4th quadrant . And In fourth quadrant , cosine and secant are positive . Therefore , the result will be positive. Now we know that ,

$\implies \sec (360^o-\theta)= \sec\theta$

Using this ,

$\implies \sec (330^o) \\\\\rm\implies sec(360^o-30^o) \\\\\rm\implies \sec 30^o$

And the value of sec 30° is ,

$\implies \sec 30^o = \dfrac{2}{\sqrt3}$

And by question we need to write it with a rational denominator .So on rationalising the denominator , we have ,

$\implies \sec 30^o = \dfrac{2}{\sqrt3}=\boxed{\red{\dfrac{2\sqrt3}{3}}}$

Hence the required answer is 2√3/3.

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Sec 330 find the exact value in simplest form with a rational denominator

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