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grin007 [14]
3 years ago
11

Simplify the trigonometric expression sec theta cos theta a. tan theta b. 1 c. cot theta d. sin theta

Mathematics
1 answer:
Rus_ich [418]3 years ago
4 0
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 \frac{1}x.

An important property of reciprocals is that if you mutliply them together they will cancel out--take \frac{4}7\times\frac{7}4 for example.

Since sec<span>Ө is literally <em>defined</em> as the reciprocal of cos</span><span>Ө, it is evident that
\boxed{\sec\Theta\cos\Theta=1}</span>
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Answer:

30 kilometers

Step-by-step explanation:

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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:

\bar x = \frac{\sum fx}{\sum f}

So, we have:

\bar x = \frac{99.5* 345 + 299.5* 97 + 499.5* 52 + 699.5 * 21 + 899.5 * 9 +  1099.5 * 8 + 1299.5 * 3}{345 + 97 + 52 + 21 + 9 + 8 +3}

Evaluate

\bar x = 233.331775701

Approximate

\bar x = 233.3

Hence, the approximation of the mean is 233.3

<h3>How to determine the standard deviation?</h3>

The standard deviation is calculated as:

\sigma = \sqrt{\frac{\sum f(x - \bar x)^2}{\sum f}}

So, we have:

\sigma= \sqrt{\frac{(99.5-233.3)^2* 345 + (299.5-233.3)^2* 97 +...... + (1299.5 -233.3)^2* 3}{345 + 97 + 52 + 21 + 9 + 8 +3}

Evaluate

\sigma = 229.82

Hence, the approximation of the standard deviation is 229.82

Read more about mean and standard deviation at:

brainly.com/question/475676

#SPJ1

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2 years ago
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I’m pretty sure it would be C
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