Simplify the trigonometric expression sec theta cos theta a. tan theta b. 1 c. cot theta d. sin theta
1 answer:
Question:<u /> <em>Simplify the trigonometric expression sec</em><span><em>Өcos</em></span><span><em>Ө.</em></span>
For each of the three basic trig functions, (sin, cos, tan) there are three more which act as their reciprocals. (csc, sec, and cot respectively)
Reciprocals, of course, are flipped fractions. If you have some number x, the reciprocal can be expressed as
.
An important property of reciprocals is that if you mutliply them together they will cancel out--take
for example.
Since sec<span>Ө is literally <em>defined</em> as the reciprocal of cos</span><span>Ө, it is evident that
</span>
For each of the three basic trig functions, (sin, cos, tan) there are three more which act as their reciprocals. (csc, sec, and cot respectively)
Reciprocals, of course, are flipped fractions. If you have some number x, the reciprocal can be expressed as
An important property of reciprocals is that if you mutliply them together they will cancel out--take
Since sec<span>Ө is literally <em>defined</em> as the reciprocal of cos</span><span>Ө, it is evident that
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The approximations of the mean and the standard deviation are 233.3 and 229.82, respectively
<h3>How to determine the mean?</h3>The table of values is given as:
Savings Lower Limit Upper Limit Frequency
0-199 0 199 345
200-399 200 399 97
400-599 400 599 52
600-799 600 799 21
800-999 800 999 9
1000-1199 1000 1199 8
1200-1399 1200 1399 3
Rewrite the table to include the class midpoint and the frequency
x f
99.5 345
299.5 97
499.5 52
699.5 21
899.5 9
1099.5 8
1299.5 3
The mean is calculated as:
So, we have:
Evaluate
Approximate
Hence, the approximation of the mean is 233.3
<h3>How to determine the standard deviation?</h3>The standard deviation is calculated as:
So, we have:
Evaluate
Hence, the approximation of the standard deviation is 229.82
Read more about mean and standard deviation at:
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