Recall the angle sum identity for cosine,
cos(α + β) = cos(α) cos(β) - sin(α) sin(β)
We're given sin(α) = -1/3 and tan(β) = 7/3. Since α terminates in quadrant IV, we know that cos(α) is positive, and since β terminates in quadrant III, both sin(β) and cos(β) are negative.
Recall the Pythagorean identities,
cos²(x) + sin²(x) = 1
and
1 + tan²(x) = sec²(x)
Using the first identity, we find
cos²(α) = 1 - sin²(α)
cos(α) = + √(1 - (-1/3)²)
cos(α) = + √(8/9)
cos(α) = √8/3
Using the second identity,
sec²(β) = 1 + tan²(β)
sec(β) = - √(1 + tan²(β))
sec(β) = - √(1 + (7/3)²)
sec(β) = - √(58/9)
sec(β) = -√58/3
cos(β) = -3/√58
Then by definition of tangent,
tan(β) = sin(β) / cos(β)
sin(β) = tan(β) cos(β)
sin(β) = (7/3) (-3/√58)
sin(β) = -7/√58
Putting everything together,
cos(α + β) = cos(α) cos(β) - sin(α) sin(β)
cos(α + β) = (√8/3) (-3/√58) - (-1/3) (-7/√58)
cos(α + β) = -(7 + 3√8)/(3√58)
❤❤goodmorning everyone, today is going to be an amazing day dont let anyone bring you down today! remember to love your self!!!❤
Answer:
Ok thank u!
Explanation:
2. Thomas wants to add a watermark to his spreadsheet and chooses a giant black plus sign.
Assuming his spreadsheet is full of enough data to cover several pages and uses plain
styling with no filling, what issue will Thomas run into? What could Thomas possibly
do to use something similar as a watermark?
Answer:
An issue Thomas might run into is..
Explanation:
Thomas might run into the issue that people will not be able to see the data.
Thomas could make the watermark a lighter color such as a light gray or even a light blue instead of black and Thomas could add filling to his styling to make it easier to see and read.
sunog na nagsulong sa pagtatag ng pamahalaang sibil sa pilipinas
(G O S U S N O P O S E R)
pasagutan po agad
Thank you po
What does it mean to be ‘other oriented’?
Answer:
The process of acting on information. What does it mean to be other -oriented? To be aware of the thoughts, needs, experiences, personality, emotions, motives, desires, culture, and goals of your communication partners while still maintaining your own integrity.
Explanation:
How are you doing today?
Answer:
great
Explanation:
Answer:
im doing ok
Explanation:
Ive had to to a lot of homework and cleaning today but hopefully it pays off :)
từ vẻ đẹp của Vũ Nương trong đoạn trích ở phần đọc - hiểu, viết đoạn văn ( khoảng 20 câu ) về những việc làm thể hiện lòng hiếu thảo của em với cha mẹ.
what is that mean about that
Describe If each statement describes England, or Spain, France and Russia.
Parliament had important powers.
Monarchs had limits on their power
Absolutism was increasing
Monarchs grew more powerful
Answer:
Look at the screenshot below.
Have a great day
Explanation:
WILL MARK BRAINLIEST IF WORK IS SHOWN
Mr. Jackson's dog Gromit jumped out of a second story window (through the screen) and fell to the ground below. The window is 15 feet high, the acceleration of gravity is 9.8m/s2, and there are 3.28 feet in each meter. What was the final velocity of this crazed dog?
Answer:
calculate with formula plz
in the second paragraph, the question with which the narrator confronts her mother (“i took....my dad”) reveals which of the following about there contrasting values?
Answer:
Matilda's anger is tempered by her mother's sense of humor. Her mother's leniency is at odds with Matilda's more objective point of view.
Explanation:
Which of the following sentences is punctuated correctly? A. Tory was waiting for her mom, at the mall, which was going to close soon. B. Tory was waiting (for her mom at the mall) which was going to close soon. C. Tory was waiting for her mom at the mall, which was going to close soon. D. Tory was waiting, for her mom at the mall—which was going to close soon.
Answer:
C is the correct sentence
There is a 20% chance it will rain today. If it rains, there is a 10% chance that we will be allowed to go outside; otherwise, there is an 80% chance we will be able to go outside. What is the probability that we will be allowed to go outside?
Answer:
82
Explanation:
20%x10%=2
80%+2% = 82%
(NEED ASAP)
Type the correct answer in each box.
In the figure, lines m and n are parallel to each other. Lines pand are also parallel to each other. 68°.
The value of x is[-------] degrees, and the value of y is [-------] degrees.
[tex]\Large \boxed{\sf y=68, x=112}[/tex]
A transversal line cuts two parallel lines, producing pairs of angles with unique features.
y. Corresponding angles are equal (68=68)
x. Angles on a straight line add up to 180 degrees (180-68=112)
Thank-you letters should be sent out within
of the interview.
O A. one week
B. one day
C. one month
D. a few days
Answer:
B. one day
Explanation:
It's best to send a thank you letter while you're still fresh in the interviewer's mind. So you should send the email message within 24 hours of the interview (the same day as the interview or the next).
Insecure but I'm working with it
Many things that I could get rid of
Ain't about to give it up
I made a few mistakes, I regret it nightly
I broke a couple hearts that I wear on my sleeve
My mama always said, girl, you're trouble
And now I wonder, could you fall for a woman like me
And every time we touch, boy, you make me feel weak
I can tell you're shy and I think you're so sweet
Spending every night under covers and
Still I wonder, how could you fall for a woman like me (A woman)
Answer:
its called women like me
Explanation:
i looked it up
When you use a match to light a candle, multiple _______ of energy occur
Answer:
transformations (missing word)
Explanation:
When you use a match to light a candle, multiple transformations of energy occur.
To light a match, mechanical energy must first be converted to thermal energy. The particles in the match release chemical energy that has been accumulated as a result of the thermal energy, which then transforms into further thermal energy and the electromagnetic energy that you see as light.
Multiple energy transformations involving mechanical, thermal, chemical, and light energy occur when you light a match.
Therefore, when you use a match to light a candle, multiple transformations of energy occur.
Lean more about the mechanical energy here:
https://brainly.com/question/35147838.
#SPJ3
Assume that a 100 cm3 soil core weighs 78g when oven-dried and 123 g when saturated. Calculate the total pore space and total porosity. Show all of you work.
To calculate the total pore space, we will find the difference between the mass of the soil when it is oven - dried and when it is saturated. Therefore, the value of the total pore space and total porosity are 45g and 45% respectively
Given that a 100 cm3 soil core weighs 78g when oven-dried and 123 g when saturated.
The given parameters are;
Volume of soil V = 100[tex]cm^{3}[/tex]
Mass ( Oven dried) [tex]M_{1}[/tex] = 78g
Mass ( Saturated) [tex]M_{2}[/tex] = 123g
In the soil formation, pore space refers to the volume of soil. And to calculate the total pore space, we will find the difference between the mass of the soil when it is oven - dried and when it is saturated. That is,
Total pore space = [tex]M_{2}[/tex] - [tex]M_{1}[/tex]
Total pore space = 123 - 78
Total pore space = 45g
And total porosity will be the percentage of the ratio of total pore space to the given volume of the soil. That is,
Total porosity = (Total pore space / volume of the soil) x 100
Total porosity = 45/100 x 100
Total porosity = 0.45 x 100
Total porosity = 45%
Therefore, the value of the total pore space and total porosity are 45g and 45% respectively
Learn more here: https://brainly.com/question/21343105
if you had one person to save in 5 sec who would it be.
Keanu Reeves :3
hes a national treasure
Which of the following is an example of Balkanization? Please Help!!!
Answer:
Yugoslavia
Explanation:
The former Yugoslavia has become five independent countries and the province of Kosovo is currently fighting to break away of what is left of Yugoslavia.
Answer:
Balkanization. The term comes from the Balkan Peninsula of Europe, a region that has balkanized may time, and is still undergoing balkanization. EXAMPLES: The former Yugoslavia has become five independent countries and the province of Kosovo is currently fighting to break away of what is left of Yugoslavia.
Pls, choose me as brainliest!
Is it bad to love someone even after you have broken up?
Answer:
Nope :)
Explanation:
I don't believe so. The heart wants what the heart wants. If you truly love that other person and not for body features then there is no shame. After all, you broke up with the other person for a reason and you already broke ties with. Do consider it might come off as if you move on too quickly but other than it's not really bad.
¿Cuál personaje desempeña el rol del "gracioso" o "donaire" en el fragmento?
Mga Batayang Salik sa pagkakaroon ng pagkakaroon ng kabihasnan
1
2
3
4
5
6
pls I need your help
Explanation:
Matatag na suplay ng pagkain.
Sosyal na istraktura.
Sistema ng pamahalaan.
Sistemang panrelihiyon.
Mataas na binuo na kultura.
Mga pag-unlad sa teknolohiya.
Mataas na binuo nakasulat na wika.
What is the quantity of books that this individual is carrying in the image provided.
Answer:
3
Hope it helps
who greets the speaker and the speakers friends
Answer:
In the poem "The Blessing" By James Wright
Explanation:the internet
What did anthropologists William and Jean O'Barr find in examining the factors that influence a
person's style of speech when testifying as a witness in court?
Answer:
Social influences somehow interfered with normal, biologically based behavior patterns to produce same-sex attraction.
Explanation:
Search What did anthropologists William and Jean O'Barr find in examining the factors that influence a
person's style of speech when testifying as a witness in court?
Your sister is looking for a way to increase the amount of money she is earning in her savings account what should she do
Answer:
a good why to make some rly good money on the side id to either sell the items u don't need nor use and also as well u can be a photographer and sell pics online or take some creative pictures for people its super easy and simple.
1) Define family life education clearly and describe its benefit briefly
Answer:
practice of education which help in the overall development of family members
Explanation:
Family life education provides great help to make family happy and to promote family welfare. The family life education helps to know about the changes seen in or body from the early age in our life.
compare relative motion and relative velocity
an action verb that is followed by a direct object
What were Austria’s aims and priorities at the congress
Answer: to reestablish peace and stability in Europe
Explanation: The goal of the conservatives at the Congress, led by Prince Klemens von Metternich of Austria, was to reestablish peace and stability in Europe. To accomplish this, a new balance of power had to be established.
Psychological tools are used to understand human behavior and psychological processes
case studies ,surveys ,naturalistic observation , and laboratory observation are examples of descriptive or correlational researches methods . using these methods researchers can describe different events ,experiences,or behaviours and look for links between them
Psychologists study mental processes and human behavior by observing, interpreting, and recording how people and other animals relate to one another and the environment. ... Research methods vary with the topic which they study, but by and large, the chief techniques used are observation, assessment, and experimentation.
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