Question

Find the exact value of sec(11pi/3) using reference angles.

Answer 1

I think a good start would be to convert sec into cos using the identity \[\sec(x) = \frac{1}{\cos(x)}\] have you tried that?

Answer 2

No lol that didnt come to me in my mind but it makes sense to do that

Answer 3

Cool, try that out and see if you can get it. Let us know if you get stuck! :)

Answer 4

im stuck still tho idk how to go on or what exactly to do

Answer 5

OK, so let's just focus on \[\cos(\frac{11 \pi}{3})\] for now.

Answer 6

Have you learned to use the unit circle?

Answer 7

yes i have

Answer 8

OK, that will make it a lot easier! :) Alright, now let's try and figure out where the angle 11pi/3 will land on the unit circle. Remember that whenever we get 2pi we've gone around the whole circle.

Answer 9

11pi/3 is 660 degrees. cos(660 degrees) = cos(300 degrees)

Answer 10

ok i know the terminal point of 11pi/3 is (1/2, -sqrt3/2)

Answer 11

good!

Answer 12

Remember then that the cosine value matches the x-coordinate, so what is the value of our cosine?

Answer 13

1/2

Answer 14

correct! :D

Answer 15

Alright, so we now know that \[\cos(\frac{11 \pi}{3}) = \frac{1}{2}\]

Answer 16

But, of course, we wanted to know what secant was. So, we just need to divide 1 by 1/2 in the beginning.

Answer 17

So, \[\frac{1}{1/2} = 1 \div \frac{1}{2} = 1 \times \frac{2}{1} = 2\]

Answer 18

and there's our answer! does that make sense? anything you want to clarify? :)

Answer 19

That makes perfect sense actually thank you! :)

Answer 20

great job!

Answer 21

Thank you!

Answer 22

yw