1 answer

How do you find the value of #sec (315)#?

Question:

How do you find the value of #sec (315)#?

Answers

#sec(315º) = sqrt(2)#

Explanation:

We have #sec(315) = 1/cos(315)#

Assuming #315# is a value in degrees, we can rewrite that to #315º = 360º-45º#, and since #360º# is a full loop, we can say that

#sec(315º) = 1/cos(-45º)#

Since the cosine is an even function, we have that #cos(-x) = cos(x)#, so

#sec(315º) = 1/cos(45º)#

#45º# is a special angle so we know that its cosine is #sqrt(2)/2#, so

#sec(315º) = 1/(sqrt(2)/2) = 2/sqrt(2) = sqrt(2)#

If it's a value in radians, we see that #315 - 100*pi ~= 0.84#, whose cosine is coincidentally #2/3# - or close to it - so

#sec(315) = 1/cos(315) ~= 1/cos(0.84) ~= 3/2#

Which is only a little bit bigger than the proper answer, approximately #1.4994#. But yeah, you can't really solve this without calculator. You could at best give a range based on the special angles, like #sec(pi/6) < sec(315) < sec(pi/3)#

.

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