If cosa = -4/5 with a in QIII. Find sin2a
2 answers:
Since a is in the third quadrant, both sina and cosa are negative.
Now, sin(2a) can be rewritten as 2sin(a)cos(a).
Thus, we can find sin(a) by using Pythagoras' Theorem.
Now, by focusing on the positive value, we can see that 5 is the hypotenuse.
Let the missing side be x.
x² + 16 = 25
x² = 9
x = 3, because x > 0
Substituting these into the equation, we get:
Now, sin(2a) can be rewritten as 2sin(a)cos(a).
Thus, we can find sin(a) by using Pythagoras' Theorem.
Now, by focusing on the positive value, we can see that 5 is the hypotenuse.
Let the missing side be x.
x² + 16 = 25
x² = 9
x = 3, because x > 0
Substituting these into the equation, we get:
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Answer:
The confidence interval for the mean is given by the following formula:
And the confidence interval is given by:
(0.123, 0.177)
And for this case the interval contains the value 0.16, so then we can conclude at 5% of significance that the true proportion is not different from 0.16
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The population proportion have the following distribution
Solution to the problem
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by and
. And the critical value would be given by:
The confidence interval for the mean is given by the following formula:
And the confidence interval is given by:
(0.123, 0.177)
And for this case the interval contains the value 0.16, so then we can conclude at 5% of significance that the true proportion is not different from 0.16