is in quadrant I, so
.
is in quadrant II, so
.
Recall that for any angle ,
Then with the conditions determined above, we get
and
Now recall the compound angle formulas:
as well as the definition of tangent:
Then
1.
2.
3.
4.
5.
6.
7. A bit more work required here. Recall the half-angle identities:
Because is in quadrant II, we know that
is in quadrant I. Specifically, we know
, so
. In this quadrant, we have
, so
8.
Answer:
a) It can be used because np and n(1-p) are both greater than 5.
Step-by-step explanation:
Binomial distribution and approximation to the normal:
The binomial distribution has two parameters:
n, which is the number of trials.
p, which is the probability of a success on a single trial.
If np and n(1-p) are both greater than 5, the normal approximation to the binomial can appropriately be used.
In this question:
So, lets verify the conditions:
np = 201*0.45 = 90.45 > 5
n(1-p) = 201*(1-0.45) = 201*0.55 = 110.55 > 5
Since both np and n(1-p) are greater than 5, the approximation can be used.