SOLUTION: Find the exact values of sec(−225∘) and sec(−5𝜋/6).

Question 1162231: Find the exact values of sec(−225∘) and sec(−5𝜋/6).
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
-225 degrees + 360 is equal to 135 degrees.
135 degrees is in the second quadrant.
180 - 135 degrees is equal to 45 degrees.
45 degrees is the reference angle.
secant of 45 degrees is equal to 1 / cosine of 45 degrees is equal to 1 / (sqrt(2) / 2.) is equal to 2 / sqrt(2).
secant is negative in the second quadrant, therefore secant(-225) = -2/sqrt(2).

-5pi/6 * 180 / pi = -150 degrees.
-150 + 360 = 210 degrees.
210 degrees is in the third quadrant.
210 - 180 = 30 degrees.
that's the reference angle.
secant of 30 degrees is equal to 1 / cosine of 30 degrees.
cosine of 30 degrees is equal to sqrt(3) / 2
1 / cosine of 30 degrees is equal to 2 / sqrt(3).
secant is negative in the third quadrant, therefore secand ot 210 degrees is equal to -2/sqrt(3).

your solutions are:
secant(-225) = -2/sqrt(2)
secant(-150) = -2/sqrt(3)

these can be seen visually in the following displays.
first is secant of -225 degrees.
second is secant of -5pi/6 radians.

note that -2/sqrt(2) is equal to -1.414 rounded to 3 decimal places and -2/sqrt(3) is equal to -1.155 rounded to 3 decimal places.

these decimal equivalents for y are shown on the graphs.

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