Can someone help me with math please?

Question

Find the exact value of:

sec(11/3pi)=
and
csc(11/3pi)=

Could you please also explain how to you found it? I can't understand the notes I wrote down. Thank you.

EDIT:

it's (11/3)pi for both.

Answer 1

If you mean 11/3pi is 11/3 times pi, then the angle 11pi/3 is coterminal with -pi/3, and you can find trig fuctions of that angle.

Answer 2

A whole bunch of people have asked about the reciprocal functions (secant, cosecant, and cotangent) recently. To do problems like this you need to know that
sec = 1/cos
csc = 1/sin
(It might also help in similar problems to know cot = 1/tan.)

Chances are you've worked with the sin and cos of multiples of pi over three already. You should know that for any multiple of pi over 3 the cosine is always 1/2 and the sine is always SQR(2)/2 (but both can be positive or negative, depending on the quadrant). 11pi/3 is in the 4th quardant, so cosine is postiive and sine is negative. That means the secant will be positive, and the cosecant will be negative.

So sec(11pi/3) = 1/ [cos(11pi/3)] = 1/ (1/2) = 2

csc(11pi/3) = 1/ [sin(11pi/3)] = 1 / -(SQR(2)/2) = -2/SQR(2) or -2SQR(2)/2 or just negative square root of 2.

One more important thing: this is assuming you mean (11/3)pi, not 11/(3pi) for your angle. You almost certainly do mean that.

Answer 3

2.54590988
1.0873944
I be all night explaining it to you