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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.
Answer:
The % Alicia speed walking is 125 % of average walking
Step-by-step explanation:
Given as :
Distance cover by Alicia while walking = 4 miles
Time taken = 1 hour
So, Speed of Alicia while walking =
Or, S 1 =
I.e S 1 = 4 mph
And
Distance cover by Alicia while speed walk = 5 miles
Time Taken = 1 hour
So, Speed of Alicia while speed walking =
Or, S 2 =
I.e S 2 = 5 mph
Or, % Rate = ×100 = 125
Hence The % Alicia speed walking is 125 % of average walking Answer