Simplify the expression as much as possible. sin(2x)cos(x)
1 answer:
For this kind of exercise you need to know the trigonometric identities.
In this case:
--->sin(2a)=2(sen(a)*cos(a))
(That comes from sin(a+b)=sin(a)*cos(b)+cos(a)*sin(b), since 2a is just a sum a a+a)
--->sin^2(a)+cos^2(a)=1
That way you can start transforming things and simplifying.
By doing that I got to: 2sin(x)*cos^2(x) (or 2sin(x)-2sin^3(x))
I attached the steps I followed as an image (I made a mistake on paper at the very end, that's a multiplication not a substraction, it's 2sin(x)*cos^2(x))
In this case:
--->sin(2a)=2(sen(a)*cos(a))
(That comes from sin(a+b)=sin(a)*cos(b)+cos(a)*sin(b), since 2a is just a sum a a+a)
--->sin^2(a)+cos^2(a)=1
That way you can start transforming things and simplifying.
By doing that I got to: 2sin(x)*cos^2(x) (or 2sin(x)-2sin^3(x))
I attached the steps I followed as an image (I made a mistake on paper at the very end, that's a multiplication not a substraction, it's 2sin(x)*cos^2(x))
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Answer:
a)
b) Median =40
c) Bimodal distribution 40,45 with a frequency of 2 for each one
Step-by-step explanation:
Part a
The statistical mean refers "to the mean or average that is used to derive the central tendency of the data in question. It is determined by adding all the data points in a population and then dividing the total by the number of points". And is defined:
And for this case if we apply this formula we got:
Part b
The median is a "measure of central tendency. To find the median, we arrange the observations in order from smallest to largest value. And we have two possible cases:
1) If there is an odd number of observations, the median is the middle value. 2) If there is an even number of observations, the median is the average of the two middle values."
So if we order the dataset we got:
31,33,39,40,40,42,44,45,45
Since we have an odd number of observation n=9, the median would be just the middle value on position 5 and for this case Median =40
Part c
The mode of a set of data values is the value that appears most often. As a set of data can have more than one mode, the mode does not necessarily indicate the centre of a data set.
For this case we have a bimodal distribution and the corresponding values are 40 and 45 with a frequency of 2 for each one.