How do I find the value of sec 330?

1 Answer
Lovecraft
Sep 17, 2015

sec(330º) = 2sqrt3/3

Explanation:

Remember that secx = 1/cosx

So
sec330º = 1/cos(330º)

Remember that cos(a-b) = cos(a)cos(b) + sin(a)sin(b) and that 330º = 360º - 30º, so

cos(330º) = cos(360º - 30º) = cos(360º)cos(30º) + sin(360º)sin(30º)

The cosine, sine, tangent and secant of 360º equal the cosine, sine, tangent and secant of 0º respectively. We know that sin0º is 0, and that cos0º = 1 so

cos(330º) = 1*cos(30º) + 0*sin(30º)
cos(330º) = sqrt3/2

So

sec(330º) = 2/sqrt3

Rationalizing,

sec(330º) = 2sqrt3/3

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