4) (a) For these problems, you should take time to familiarize yourself with common fractions that appear on the unit circle. $\frac{\sqrt{3}} {3}$ 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.

7 0

3 years ago