How do I find out values of stuff like "sec(pi/3)" without a calculator?

Question

Calculus 2 professor doesn't let us use a calculator for tests.

I know the basic values of cos/sin of 0, pi, pi/2,3pi/2 and 2pi. by imagining it in the unit circle as coordinates of 1's and 0's.

I also know that tan of pi would be (sin pi/ cos pi) which is equal to 0.

I'm also familiar with the basic inverse properties like sec = 1/cos.

So how about crazy values cos(pi/3) or sin (7 pi/4)?

Thank you guys so much for the help.

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Answer 1 · 2018-06-27T01:00:19

#sec(pi/3)=2#

#pi/3# radians is #60^o#, which is a standard angle whose trigonometric values should be learnt for instant recall.

So, we have:

#cos(pi/3)=1/2#

Hence:

#sec(pi/3)=2#