Ask question

Ask question

All categories

3 years ago

12

Write the following expression as a function of a positive acute angle. Use "+" to indicate a positive value and "-" to indicate

a negative value.

2 answers:

Sauron [17]3 years ago

6 0

Answer:

As property of trigonometric cosine function, we have:

cos(x) = cos(-x)

=> cos(-240) = cos(240)

Otherwise, we also have:

cos(x + 180) = -cos(x)

=> cos(240) = - cos(60)

=> cos(-240) = cos(+240) = -cos(+60)

Hope this helps!

:)

Goshia [24]3 years ago

3 0

Since the trigonometric functions are periodic, we know that

$\cos(x)=\cos(x+360)$

In this case, you have

$\cos(-240)=\cos(-240+360)=\cos(120)$

Finally, we have

$\cos(120)=\cos(90+30)$

and you can use the formula

$\cos(90+x)=-\sin(x)$

To conclude

$\cos(120)=\cos(90+30)=-\sin(30)$

You might be interested in

The probability that a randomly selected 3-year-old male chipmunk will live to be 4 years old is 0.96516.

mezya [45]

Using the binomial distribution, it is found that there is a:

a) The probability that two randomly selected 3-year-old male chipmunks will live to be 4 years old is 0.93153 = 93.153%.

b) The probability that six randomly selected 3-year-old male chipmunks will live to be 4 years old is 0.80834 = 80.834%.

c) The probability that at least one of six randomly selected 3-year-old male chipmunks will not live to be 4 years old is 0.19166 = 19.166%. This probability is not unusual, as it is greater than 5%.

-----------

For each chipmunk, there are only two possible outcomes. Either they will live to be 4 years old, or they will not. The probability of a chipmunk living is independent of any other chipmunk, which means that the binomial distribution is used to solve this question.

Binomial probability distribution

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$C_{n,x} = \frac{n!}{x!(n-x)!}$

The parameters are:

x is the number of successes.
n is the number of trials.
p is the probability of a success on a single trial.

In this problem:

0.96516 probability of a chipmunk living through the year, thus $p = 0.96516$

Item a:

Two is P(X = 2) when n = 2, thus:

$P(X = 2) = C_{2,2}(0.96516)^2(1-0.96516)^{0} = 0.9315$

The probability that two randomly selected 3-year-old male chipmunks will live to be 4 years old is 0.93153 = 93.153%.

Item b:

Six is P(X = 6) when n = 6, then:

$P(X = 6) = C_{6,6}(0.96516)^6(1-0.96516)^{0} = 0.80834$

The probability that six randomly selected 3-year-old male chipmunks will live to be 4 years old is 0.80834 = 80.834%.

Item c:

At least one not living is:

$P(X < 6) = 1 - P(X = 6) = 1 - 0.80834 = 0.19166$

The probability that at least one of six randomly selected 3-year-old male chipmunks will not live to be 4 years old is 0.19166 = 19.166%. This probability is not unusual, as it is greater than 5%.

A similar problem is given at brainly.com/question/24756209

6 0

3 years ago

A farmer want to fence in a rectangular field that encloses 3600 sq feet. The cost 3.50 per foot. Express the total cost c(x) of

Alexeev081 [22]

Answer:

Answers is C (x)=3.50 {x+3600/x} -_-

Step-by-step explanation:

8 0

3 years ago

In a study, the sample is chosen by pulling 50 names from a hat What is the sampling method?

Irina18 [472]

Answer:Simple random sample

Step-by-step explanation:

A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen. A simple random sample is meant to be an unbiased representation of a group.

NOTE:

No easier method exists to extract a research sample from a larger population than simple random sampling. Selecting subjects completely at random from the larger population also yields a sample that is representative of the group being studied.

6 0

3 years ago

Please help with 4-9!!!

olya-2409 [2.1K]

sdfsdf

4) $\frac{3m+15}{2} = 22.5$

Multiply by 2 on both sides

3m + 15 = 45

Subtract both sides by 15

3m = 30

Divide both sides by 3

so m = 3

5) $21= \frac{q+35}{8}$

Multiply both sides by 8

168 = q + 35

Subtract both sides by 35

q = 133

6) $14 + \frac{4z}{-11} = 66$

Subtract 14 from both sides

$\frac{4z}{-11} = 52$

multiply by -11 on both sides

4x = 572

Divide both sides by 4

x= 143

7) $\frac{3}{5} c - 6 = 9$

Add 6 on both sides

$\frac{3}{5} c = 15$

Multiply both sides by 5

3c = 75

Divide both sides by 3

c = 25

8) $\frac{t}{-2} + 17 = -9$

Subtract both sides by 17

$\frac{t}{-2} =26$

Multiply both sides by -2

t = -52

9) $-6 = \frac{5p-(-2)}{-7}$

Multiply both sides by -7

42= 5p + 2

subtract 2 from both sides

40 = 5p

Divide both sides by 5

so p = 8

6 0

3 years ago

Read 2 more answers

Daily high temperatures in St. Louis for the last week were as follows: 95, 92, 93, 92, 95, 90, 90 (yesterday). a) The

hichkok12 [17]

Answer:

a) T = 91.7 degrees

b) T = 90 degrees

c) MAD = 1.9

d) MSE = 5.05

Step-by-step explanation:

Given:

- Daily high temperatures in St. Louis for the last week were as follows:

95, 92, 93, 92, 95, 90, 90

Find:

a) Forecast the high temperature today, using a 3-day moving average.

b) Forecast the high temperature today, using a 2-day moving average.

c) Calculate the mean absolute deviation based on a 2-day moving average, covering all days in which you can have a forecast and an actual temperature.

d) The mean squared error for the 2-day moving average

Solution:

a)

- The set of 3 day moving average is as follows:

4. (95 + 92 + 93) ÷ 3 = 93.33⁰C

5. (92 + 93 + 92) ÷ 3 = 92.33⁰C

6. (93 + 92 + 95) ÷ 3 = 93.33⁰C

7. (92 + 95 + 90) ÷ 3 = 92.33⁰C

8. (95 + 90 + 90) ÷ 3 = 91.667⁰C

- Now use these points on excel sheet to forecast the temperature for today. The line of best fit is given:

T = 91.7 degrees

b)

- The set of 2 day moving average is as follows:

3. (95 + 92) ÷ 2 = 93.5⁰C

4. (95 + 93) ÷ 2 = 92.5⁰C

5. (93 + 92) ÷ 2 = 92.5⁰C

6. (92 + 95) ÷ 2 = 93.5⁰C

7. (95 + 90) ÷ 2 = 92.5⁰C

8. (90 + 90) ÷ 2 = 90⁰C

- Now use these points on excel sheet to forecast the temperature for today. The line of best fit is given:

T = 90 degrees

c)

Error Error^2

3. 93.5⁰C 0.5 0.25

4. 92.5⁰C 0.5 0.25

5. 92.5⁰C 2.5 6.25

6. 93.5⁰C 3.5 12.25

7. 92.5⁰C 2.5 6.25

8. 90⁰C

- The mean absolute deviation as follows:

MAD = Sum of all errors / 5

MAD = (0.5+0.5+2.5+3.5+2.5) / 5

MAD = 1.9

d)

- The mean squared error deviation as follows:

MSE = Sum of all error^2 / 5

MSE = (0.25+0.25+6.25+12.25+6.25) / 5

MSE = 5.05

4 0

3 years ago