evaluate exactly sec 135*?

Answer 1

the reference number for 135 degrees is 45 degrees and is found in quadrant 2
sec 45 is also the same as
1/(cos45)
if cos 45 is
sqrt(2)/2 (but since it is found in the second quadrant it would be
-sqrt(2)/2
1/(-sqrt(2)/2) would be
-2/(sqrt(2)
which can also be written as
-sqrt(2)
thus your answer is

-sqrt(2)

Answer 2

sec (x) = 1 / cos (x)
sec 135° = 1 / cos 135°
sec 135° = 1 / -sin 45°
sec 135° = 1 / (-1/√2)
sec 135° = -(√2)

Answer 3

135 = 90 + 45 = pi/2 + pi/4 = 3pi/4


sec = 1/cos

So, the cosine of 3pi/4 = -cosine pi/4, right?

cosine pi/4 = 1/sqrt(2)

Therefore, secant 3pi/4 = -sqrt(2)

The word 'exact' implys that you should leave it in the root form.

Btw, pi/4, pi/3, pi/2, pi, and additions of pi/2 and pi are angles that you'll encounter a lot.