How do I find the value of sec 330?

gretelovsky0gn

gretelovsky0gn

Answered question

2023-02-11

How do I find the value of sec 330?

Answer & Explanation

Sydnee Glover

Sydnee Glover

Beginner2023-02-12Added 6 answers

Remember that sec x = 1 cos x
So
sec 330 º = 1 cos ( 330 º )
Remember that cos ( a - b ) = cos ( a ) cos ( b ) + sin ( a ) sin ( b ) and that 330 º = 360 º - 30 º , so
cos ( 330 º ) = cos ( 360 º - 30 º ) = cos ( 360 º ) cos ( 30 º ) + sin ( 360 º ) sin ( 30 º )
The 360o cosine, sine, tangent, and secant are equivalent to the 0o cosine, sine, tangent, and secant. We know that sin 0 º is 0, and that cos 0 º = 1 so
cos ( 330 º ) = 1 cos ( 30 º ) + 0 sin ( 30 º )
cos ( 330 º ) = 3 2
So
sec ( 330 º ) = 2 3
Rationalizing,
sec ( 330 º ) = 2 3 3

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