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ElenaW [278]
2 years ago
13

Find the exact value of sec 330° in simplest form with a rational denominator.

Mathematics
2 answers:
Juli2301 [7.4K]2 years ago
8 0

Answer:

\implies \sec 330^o = \dfrac{2}{\sqrt3}=\dfrac{2\sqrt{3}}{3}

Step-by-step explanation:

<u>Given :- </u>

  • \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

<u>Using this , </u>

\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}}}

<u>Hence the required answer is 2√3/3.</u>

Levart [38]2 years ago
7 0

Answer:

2√3/3

Step-by-step explanation:

Sec(330°)

=1/cos(330°)

=1/√3/2 (since Cos (330°)=√3/2

=1×2/√3

=2/√3×√3/√3

=2√3/3

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