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Find the exact value of csc 330° in simplest form with a rational denominator-

Sagot :

The answer is -2 for the csc and it’s also a rational denominator
VirαtKσhli

Answer:

[tex]\implies \cosec 330^o = -2[/tex]

Step-by-step explanation:

Given :-

  • [tex]\cosec 330^o [/tex]

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 and the rest are negative .So cosecant will be negative . Therefore , the result will be -ve. Now we know that ,

[tex]\implies \cosec (360^o-\theta)= -\cosec\theta [/tex]

Using this ,

[tex]\implies \cosec (330^o) \\\\\rm\implies cosec(360^o-30^o) \\\\\rm\implies - \cosec 30^o [/tex]

And the value of cosec 30° is ,

[tex]\implies -\cosec 30^o = \boxed{\red{-2}}[/tex]

Hence the required answer is -2 .

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