1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Anna007 [38]
3 years ago
14

Find sin(a+b) if tan(a)=7/24 where a is in the third quadrant

Mathematics
1 answer:
ludmilkaskok [199]3 years ago
8 0
The complete question in the attached figure

we have that
tan a=7/24    a----> III quadrant
cos b=-12/13   b----> II quadrant
sin (a+b)=?

we know that
sin(a + b) = sin(a)cos(b) + cos(a)sin(b<span>)
</span>
step 1
find sin b
sin²b+cos²b=1------> sin²b=1-cos²b----> 1-(144/169)---> 25/169
sin b=5/13------> is positive because b belong to the II quadrant

step 2
Find sin a and cos a
tan a=7/24
tan a=sin a /cos a-------> sin a=tan a*cos a-----> sin a=(7/24)*cos a
sin a=(7/24)*cos a------> sin²a=(49/576)*cos²a-----> equation 1
sin²a=1-cos²a------> equation 2
equals 1 and 2
(49/576)*cos²a=1-cos²a---> cos²a*[1+(49/576)]=1----> cos²a*[625/576]=1
cos²a=576/625------> cos a=-24/25----> is negative because a belong to III quadrant
cos a=-24/25
sin²a=1-cos²a-----> 1-(576/625)----> sin²a=49/625
sin a=-7/25-----> is negative because a belong to III quadrant

step 3
find sin (a+b)
sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
sin a=-7/25
cos a=-24/25
sin b=5/13
cos b=-12/13
so
sin (a+b)=[-7/25]*[-12/13]+[-24/25]*[5/13]----> [84/325]+[-120/325]
sin (a+b)=-36/325

the answer is
sin (a+b)=-36/325

You might be interested in
The total cost (c) in dollars of renting a car for n days is given by the inequality LaTeX: c\ge125+50nc ≥ 125 + 50 n. What is t
zysi [14]

Answer:

<h3>6 days</h3>

Step-by-step explanation:

Given the inequality expression of the total cost (c) in dollars of renting a car for n days as c ≥ 125 + 50n

To get the maximum number of days for which a car could be rented if the total cost was $425, substitute c = 425 into the expression and find n

425 ≥ 125 + 50n

Subtract 125 from both sides

425 - 125 ≥ 125 + 50n  - 125

300≥ 50n

Divide both sides by 50

300/50≥50n/50

6 ≥n

Rearrange

n≤6

<em>Hence the maximum number of days for which a car could be rented if the total cost was $425 is 6days</em>

<em></em>

5 0
3 years ago
Начало сказки "Снежная королева" на 20 странице, а конец на 50.
natta225 [31]

If you start on page 20 and end on Page 50, you will have read 31 pages. I just counted from 20 to 50, including the number 20 in it.

OR: You already know there are 50-20=30 pages. But that's without counting the 20 in it. So when you add the extra 20: 30 + 1 = 31

Translated version:

Если вы начнете со страницы 20 и закончите со страницы 50, вы прочтете 31 страницу. Я только что насчитал от 20 до 50, включая число 20 в нем.

ИЛИ: Вы уже знаете, что 50-20 = 30 страниц. Но это без учета 20 в нем. Поэтому, когда вы добавляете дополнительные 20: 30 + 1 = 31

Я использовал Google Translate, поэтому результаты могут быть неточными.

7 0
3 years ago
The area of a rectangle is represented with the expression (18x-12) inches squared. The width of the rectangle is 6 inches. Writ
Rudik [331]
Are equation for a rectangle is area = (width x length)

(18x - 12) = 6 x length
length = (18x - 12) / 6
length = 3x - 2
5 0
3 years ago
Find the side length. Round to the nearest tenth if necessary.<br> 15
Rasek [7]

Answer:

x = 39

Step-by-step explanation:

This is pythagoras

x = √36² + 15²

x = √1296 + 225

x = √1521

x = 39

Hopefully it helps you

Ask if u don't understand

8 0
3 years ago
a) Everyone on the team talks until the entire team agrees on one decision. O b) Everyone on the team discusses options and then
insens350 [35]

Answer:

a) Everyone on the team talks until the entire team agrees on one decision.

Step-by-step explanation:

Option B consists of voting and not everyone would like the outcome. Option C is making an outsider the decision maker, which can't be helpful since he / she won't have as strong opinions as the team itself. Option D is just plain wrong as it defeats the purpose of team work and deciding as one team. So, I believe option A makes the most sense

8 0
2 years ago
Other questions:
  • Solution what is the area of the park in square feet
    12·1 answer
  • HELP ASAP URGENT
    14·1 answer
  • (a) Find parametric equations for the line through (3, 1, 8) that is perpendicular to the plane x − y + 4z = 7. (Use the paramet
    15·1 answer
  • A boy wins a carnial games 50% of the time. He uses a spinnser with equal-sized sections labeled 0 - 9 to simulate trials of the
    9·2 answers
  • Find the equation for a parabola with its focus at (0, 3) and a directrix of y = -3.
    7·1 answer
  • What's an expression with a value of 12
    9·2 answers
  • Abi is driving from Italy to Paris (Texas, that is). The coordinates are shown below on his map. He knows there is a rest stop b
    13·1 answer
  • What is one<br>plus two?​
    9·2 answers
  • During a football game, Max had gained 15 yards and then gained 8 more yards. Later in
    11·2 answers
  • A jewelry box contains two gold hoop earrings and two silver hoop earrings. You randomly choose two earrings. What is the probab
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!