How do you use special angles to find the ratios of sec 180 degrees?

1 Answer
Alan P.
Nov 12, 2015

#sec(180^@) = -1#

Explanation:

#180^@# has a reference angle of #0^@# and falls along the negative X-axis.

#sec= 1/cos = ("hypotenuse")/("adjacent")

#color(white)("XXX")#the #"hypotenuse"# is always positive.
#color(white)("XXX")#the #"adjacent"# is the X-axis value and along the negative X-axis it is negative.

For an angle of #0^@# the lengths of the #"hypotenuse"# and #"adjacent"# sides are equal.

Therefore #sec(180^@) = -sec(0^@) = -1#

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