SOLUTION: determine the specified trigonometric ratio for each special angle. 1. cos(11pi/6) 2.cot(5pi/4) 3.sec(4pi/3)

Algebra ->  Trigonometry-basics -> SOLUTION: determine the specified trigonometric ratio for each special angle. 1. cos(11pi/6) 2.cot(5pi/4) 3.sec(4pi/3)       Log On


   

Question 1158031: determine the specified trigonometric ratio for each special angle.
1. cos(11pi/6)
2.cot(5pi/4)
3.sec(4pi/3)
Found 2 solutions by josmiceli, Theo:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1)
+cos%28+11pi%2F6+%29+
+11pi%2F6+=+12pi%2F6+-+pi%2F6+
+11pi%2F6+=+2pi+-+pi%2F6+
This is in the 4th quadrant & the cos is positive
+cos%28+11pi%2F6+%29+=+sqrt%283%29+%2F+2+
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(2)
+cot%28+5pi%2F4+%29+
+5pi%2F4+=+4pi%2F4+%2B+pi%2F4+
+5pi%2F4+=+pi+%2B+pi%2F4+
This is in the 3rd quadrant & cot is positive (-) / (-) = (+)
+cot%28+5pi%2F4+%29+=+1%2F1+
+cot%28+5pi%2F4+%29+=+1+
------------------------------------
(3)
+sec%28+4pi%2F3+%29+
+4pi%2F3+=+3pi%2F3+%2B+pi%2F3+
+4pi%2F3+=+pi+%2B+pi%2F3+
This its in the 3rd quadrant & the sec is negative
+sec%28+4pi%2F3+%29+=+2%2F%28-1%29+
+sec%28+4pi%2F3+%29+=+-2+
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Get a 2nd opinion if needed


Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
11pi/6 radians * 180 / pi = 11*180/6 = 11*30 = 330 degrees.
the angle is in the fourth quadrant.
the reference angle = 360 - 330 = 30 degrees.
cosine of 30 degrees = sqrt(3)/2
since the angle is in the fourth quadrant, cosine is positive, therefore the cosine of 330 degrees is sqrt(3)/2.

5pi/4 radians * 180 / pi = 5 * 180 / 4 = 5 * 45 = 225 degrees.
the angle is in the third quadrant.
the reference angle is 225 - 180 = 45 degrees.
cotangent of 45 degrees = 1 / tangent of 45 degrees = 1
since the angle is in the third quadrant, cotangent is positive, therefore the cotangent of 225 degrees is 1.


4pi/3 radians * 180 / pi = 4 * 180 / 3 = 4 * 60 = 240 degrees.
the angle is in the third quadrant.
the reference angle is 240 - 180 = 60 degrees.
secant of 60 degrees = 1 / cosine of 60 degrees = 1 / (1/2) = 2
since the angle is in the third quadrant, the secant is negative, therefore the secant of 240 degrees = - 2

to confirm, put your calculator in radian mode and do the following:
cos(11pi/6)
1/tan(5pi/4)
1/cos(4pi/3)

you will get:
cos(11pi/6) = .8660254038
1/tan(5pi/4) = 1
1/cos(4pi/3) = -2

enter sqrt(3)/2 in your calculator to find that it is equivalent to .8660254038 in decimal format.