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
Answer:
[tex]\implies \sec 330^o = \dfrac{2}{\sqrt3}=\dfrac{2\sqrt{3}}{3}[/tex]
Step-by-step explanation:
Given :-
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 ,
[tex]\implies \sec (360^o-\theta)= \sec\theta [/tex]
Using this ,
[tex]\implies \sec (330^o) \\\\\rm\implies sec(360^o-30^o) \\\\\rm\implies \sec 30^o [/tex]
And the value of sec 30° is ,
[tex]\implies \sec 30^o = \dfrac{2}{\sqrt3}[/tex]
And by question we need to write it with a rational denominator .So on rationalising the denominator , we have ,
[tex]\implies \sec 30^o = \dfrac{2}{\sqrt3}=\boxed{\red{\dfrac{2\sqrt3}{3}}}[/tex]
Hence the required answer is 2√3/3.
