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.
Length of a wire = 23 cm
Given that :
▪︎The wire was cut into two pieces.
▪︎The longer piece of wire is 7 cm longer than the shorter piece of wire.
Let the shorter piece of wire be x.
Then, the longer piece of wire = x+7
An equation that can be derived from these statements :
▪︎x + x + 7 = 23
Let us solve this equation :
![= \tt x + x +7 = 23](https://tex.z-dn.net/?f=%20%3D%20%5Ctt%20x%20%20%2B%20x%20%2B7%20%20%3D%2023)
![= \tt 2x + 7 = 23](https://tex.z-dn.net/?f=%20%3D%20%5Ctt%202x%20%2B%207%20%3D%2023)
![= \tt 2x = 16](https://tex.z-dn.net/?f=%20%3D%20%5Ctt%202x%20%3D%2016)
![= \tt x = \frac{16}{2}](https://tex.z-dn.net/?f=%20%3D%20%5Ctt%20x%20%3D%20%20%5Cfrac%7B16%7D%7B2%7D%20)
![\color{plum} \hookrightarrow \color{plum}x = 8](https://tex.z-dn.net/?f=%20%5Ccolor%7Bplum%7D%20%5Chookrightarrow%20%20%5Ccolor%7Bplum%7Dx%20%3D%208)
Thus, the value of x = 8.
Which means :
Length of the shorter piece of wire = 8 cm
Length of the longer piece of wire = 8 + 7 = 15 cm
Since the length of the two wires add up to form 23 cm(8+15=23), we can conclude that we have found out the correct measures of each wire.
Therefore, the length of the shorter piece of wire = <u>8 cm</u>
Since the total amount of games played is 112, we have to divide 20 (how many games they lost during that season) by 112 and multiply that by 100 to find the percent of the games that they lost.
<em>Work:</em>
<em>20/112 is approximately 0.1786 in decimal form, so to convert that into a percentage, we multiply that by 100.</em>
<em />
<em>0.1786 x 100 = 17.86</em>
Answer:
The spurs lost about 17.86% of their games during the 2006 basketball season.
Hopefully that helps!
10 3/5=10.6
10.6+12.5=23.1
35.0-23.1=11.9
It is 11.9 miles from Chester to Durbin.