How do you use special angles to find the ratios of csc 315 degrees?

1 Answer
Alan P.
Oct 17, 2015

#315^@ = 45^@# less than a full circle
#color(white)("XXX")#i.e. #315^@-= -45^@#
#csc(-45^@) =1/sin(-45^@)=-1/sin(45^@)= -sqrt(2)#

Explanation:

Since #(-45^@)# is in Quadrant IV, #sin# (and therefore #csc#) is negative.

The #45^@# angle is a no-right angle in a right-angled equilateral triangle. If the equal length arms of the triangle are of length 1, then the hypotenuse is of length #sqrt(2)# (Pythagorean Theorem).

#sin = ("opposite")/("hypotenuse")#
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