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3 years ago

Find $\sin D$ , $\sin E$ , $\cos D$ , and $\cos E$ . Write each answer as a fraction in simplest form.

Mathematics

1 answer:

Serga [27]3 years ago

3 0

The value of sinD, sin E and cos D are 4/5, 3/5 and 3/5 respectively

<h3>SOH CAH TOA identity</h3>

According to SOH CAH TOA identity;

sin theta = opp/hyp
cos theta = adj/hyp
tan theta = opp/adj

From the figure

Hypotenuse = 15

For sinm<D

sin D = EF/DE
sin D = 12/15

sinD = 4/5

For the trig function sin E

sin E = FD/DE
Sin E = 9/15

sinE = 3/5

For the trig function cos D:

cos D = FD/DE
cos D = 9/15

cos D = 3/5

Hence the value of sinD, sin E and cos D are 4/5, 3/5 and 3/5 respectively

Learn more on trigonomtry here: brainly.com/question/24349828

You might be interested in

How many minutes he does arm routine and abdominal routine

AlekseyPX

Let $x$ be the amount of time it takes to perform an arm routine and $y$ be the amount of time it takes to perform an abdominal routine. We see:

$4x+y=70$
$4x+2y=100$

Subtracting the second equation from the first gives $y=30$ . Substituting gives $4x+30=70$ , so $4x=40$ and $x=10$ .

Thus, an arm routine takes ten minutes and an abdominal routine takes thirty minutes.

5 0

4 years ago

Which statement describes the symmetry of the data in the two box plots?

inysia [295]

Answer:

The data in country B are more symmetric than the data in country A.

Step-by-step explanation:

The following information is missing:

<em>The box plots show the average wind speeds, in miles per hour, for various cities in two different countries. Average Wind Speeds of Cities in Country A 2 box plots. The number line goes from 1 to 11. For the average wind speeds of cities in country A, the whiskers range from 1 to 9.5, and the box ranges from 3 to 7. A line divides the box at 4. For the average wind speeds of cities in country B, the whiskers range from 1.2 to 11, and the box ranges from 4 to 9. A line divides the box at 6. Average Wind Speeds of Cities in Country B</em>

Country A

minimum: 1

quartile 1: 3

median: 4

quartile 3: 7

maximum: 9.5

Country B

minimum: 1.2

quartile 1: 4

median: 6

quartile 3: 9

maximum: 11

We can see that the difference between quartile 1 and minimum, median and quartile 1, quartile 3 and median, and maximum and quartile 3 is more homogeneous in Country B than Country A, then Country B is more symmetric.

3 0

4 years ago

Read 2 more answers

A study was conducted to measure the effectiveness of hypnotism in reducing pain. The measurements are centimeters on a pain sca

blondinia [14]

The confidence interval for mean of the "before-after" differences is $\fbox{(-0.4037,1.8037)}$

Further explanation:

Find the difference between the before pain and the after pain.

Difference = before-after

Kindly refer to the Table for the difference of between the before and after pain.

Sum of difference = $5.6$

Total number of observation = $8$

Mean of difference = $0.7$

Sample standard deviation $s$ = $1.3201$

Level of significance = $5\%$

Formula for confidence interval = $\left( \bar{X} \pm t_{n-1, \frac{\alpha}{2}\%} \frac{s}{\sqrt{n}} \right)$

confidence interval = $\left( 0.7 \pm t_{8-1, \frac{5}{2}\%} \frac{1.3201}{\sqrt{8}} \right)$

confidence interval = $\left( 0.7 \pm t_{7, \frac{5}{2}\%} \frac{1.3201}{\sqrt{8}} \right)$

From the t-table.

The value of $t_{7, \frac{5}{2}\%$ = $2.365$

Confidence interval = $( 0.7 \pm 2.365}\times \frac{1.3201}{\sqrt{8}}) \right)$

Confidence interval = $\left( 0.7 - 2.365}\times \0.4667,0.7 + 2.365}\times \0.4667) \right$

Confidence interval = $(0.7-1.1037,0.7+1.1037)$

Confidence interval = $\fbox{(-0.4037,1.8037)}$

The $95\%$ confidence interval tells us about that $95\%$ chances of the true mean or population mean lies in the interval.

Yes, the hypnotism appear to be effective in reducing pain as confidence interval include includes the positive deviation from the mean.

Learn More:

1. Learn more about equation of circle brainly.com/question/1506955

2. Learn more about line segments brainly.com/question/909890

Answer Details:

Grade: College Statistics

Subject: Mathematics

Chapter: Confidence Interval

Keywords:

Probability, Statistics, Speed dating, Females rating, Confidence interval, t-test, Level of significance , Normal distribution, Central Limit Theorem, t-table, Population mean, Sample mean, Standard deviation, Symmetric, Variance.