Describe, in your own words, the identity sin^2(x) + cos^2(x) = 1.

Look at the attached figure. We define the unit circle as a circle with center in the origin (0,0) and radius 1.

Then, we consider a point P on the circumference. We call the angle between the positive half of the x axis and the radius AP.

We define

As you can see, ACD is a right triangle, and so we have

But since we know that AD is the cosine, AC is the sine, and AP is the radius (which is 1, and remains 1 when squared), we have just found out that

Here is a copy paste-able, Edg2021 friendly version of the above answer^ :)

I defined the unit circle as a circle with center A in the origin (0,0) and radius 1. Then, I considered a point P on the circumference. I call a the angle between the positive half of the x axis and the radius AP. I defined that

cos(a)= line AD, sin(a)= line AC

ACD is a right triangle, and so,

 line AD^2+ line AC^2 = line AP^2

But since I knew that AD is the cosine, AC is the sine, and AP is the radius (which is 1, and remains 1 when squared), I found that

cos(a)^2 + sin(a)^2 = 1

see below

step-by-step explanation:

7.   there are 10 data points in the set.   the middle point is between 5 and 6.   the middle point in the top half is 8   and the middle point in the bottom half is 3. to find the iqr , take point 8 and subtract point 3

mid term   point 8 = 100   point 3 = 88

iqr = 100-88 = 12

final   point 8 = 93   point 3 = 78

iqr = 93 - 78 = 15

the final has the greatest iqr

6.   b - there is a high data value that causes the data set to be asymmetrical for the males: the data for males are high and asymmetrical .   there is an outlier for the males that skews the data

5.   the   iqr is a better measure of spread for the movies and basketball games.   since the basketball game has an outlier, we do not want to use standard deviation for measurement.  

3.   the exam median is much higher than the class median.   the median line is farther to the right on the exams

2.   there is no way to tell what the means are from the box and whisker plots.  

step-by-step explanation: