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4) (a) For these problems, you should take time to familiarize yourself with common fractions that appear on the unit circle. does not appear in the unit circle unless you take the quotient 1/2 divided by sqrt(3)/2 which gives you 1/sqrt(3) which is the same as sqrt(3)/3. So our numerator is 1/2 and our denominator is sqrt(3)/2.
And remember tangent is just sin/cos. So what degree has sinx as 1/2 and and cosx as sqrt(3)/2? Well, 30 degrees does, but 30 degrees is not within the range we are given. That means they are looking for a sinx that gives us -1/2 and a cosx that gives us -sqrt(3)/2 and that is 210 degrees.
And 210 degrees in radians is 7pi/6.
I hoped that made sense.
(b) This is a lot easier. What angle gives us a cos x of -sqrt(3)/2? According to the unit circle, 150 degrees and 210 degrees does. They usually want these in radians, so the answer is 5pi/6 and 7pi/6, respectively.
5) What quadrant is radian measure 5 in?
Well 2pi or roughly 6.28 is a full circle. And 5 is slightly less than 6.28, so it is probably in quadrant IV.
But to be sure let's change 5 radian to degrees:
5 * 180/pi = 900/pi = 286.48 degrees
286.48 degrees is definitely in Q4, so we are correct.
15. They are still 6 blocks away from each other.
16. (-6,1) art and (-6,-2) animal. They are the same distance from each other as before because they moved together the same distance right to left across the coordinate plane.
17. The new location is (3,2). It is 8 blocks away from the old.
18.
A. I have attached the graph.
B. A triangle
C.
Hope that helps
16. (-6,1) art and (-6,-2) animal. They are the same distance from each other as before because they moved together the same distance right to left across the coordinate plane.
17. The new location is (3,2). It is 8 blocks away from the old.
18.
A. I have attached the graph.
B. A triangle
C.
Hope that helps