Find the exact value of each of the following. You must justify your answer in some way. (b) sin(4?/3) (c) tan(11?/6) d) csc(-5?/4) e) sec(48?/3) f) cos(-11?/3) Solution Sin(4pi/3) = -sqrt 3/2 4pi/3 = pi + pi/3 So, we get sin(pi+ pi/3) As it is in 3rd quadrant, sin is negative So, it becomes - sin pi/3 which is equals to - sqrt 3/2. c.) tan (11pi/6) = - 1/ sqrt 3 tan 11 pi /6 = tan(2pi - pi/6) tan is negative in 4th quadrant. So, we get - tan pi/6 = - 1/ sqrt 3 d.) csc(-5pi/4) = sqrt 2 csc(-x) = - csc x So, we get -csc(5pi/4) = - csc(pi + pi/4) = csc(pi/4) = sqrt 2.

1. Find the exact value of each of the following. You must justify your answer in some way.
(b) sin(4?/3)
(c) tan(11?/6)
d) csc(-5?/4)
e) sec(48?/3)
f) cos(-11?/3)
Solution
Sin(4pi/3) = -sqrt 3/2
4pi/3 = pi + pi/3
So, we get sin(pi+ pi/3)
As it is in 3rd quadrant, sin is negative
So, it becomes - sin pi/3 which is equals to - sqrt 3/2.
c.) tan (11pi/6) = - 1/ sqrt 3
tan 11 pi /6 = tan(2pi - pi/6)
tan is negative in 4th quadrant.
So, we get - tan pi/6 = - 1/ sqrt 3
d.) csc(-5pi/4) = sqrt 2
csc(-x) = - csc x
So, we get -csc(5pi/4)
= - csc(pi + pi/4)
= csc(pi/4)
= sqrt 2