ANSWER
EXPLANATION
We want to solve
where
We reciprocate both sides of this trigonometric equation to obtain:
We take arctangent of both sides to get;
This is the principal solution.
The tangent ratio is also positive in the third quadrant.
The solution in the third quadrant is
Answer:
a. 125.0714; 11.1835.
b. 109.4375; 10.4612.
Step-by-step explanation:
Given the following data;
70, 65, 71, 78, 89, 68, 50, 75.
<em>Mean = 70.75</em>
The deviation for the mean of the data is -0.75, -5.75, 0.25,7.25,18.25,-2.75,-20.75, and 4.25.
We would then find the square of this deviation;
= 875.5
Next is to find the population variance;
<em>Variance, V = 109.4375 </em>
The population standard deviation is the square root of the population variance;
<em>Standard deviation, Sd = 10.4612</em>
To find the sample variance;
<em>Variance, V = 125.0714</em>
The sample variance is;
<em>Standard deviation, Sd = 11.1835</em>
<em>Therefore, </em>
<em>a. The sample variance is 125.0714 and the sample standard deviation is 11.1835.</em>
<em>b. If this is a population data, the population variance is 109.4375 and the population standard deviation is 10.4612.</em>