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
S_A_V [24]
3 years ago
9

A+B-C=3pi then find sinA+sinB-sinC

Mathematics
1 answer:
steposvetlana [31]3 years ago
7 0
The answer:
the full question is as follow:

if A+B-C=3pi, then find sinA+sinB-sinC

first, the main formula of sine and cosine are:
sinC = 2sin(C/2)cos(C/2)
sinA +sinB = 2sin[(A+B)/2]cos[(A-B)/2]

therefore: 
 sinA+sinB-sinC = 2sin[(A+B)/2]cos[(A-B)/2] - 2sin(C/2)cos(C/2)

sin[(A+B)/2] = cos(C/2)
2sin(C/2)cos(C/2) = cos[(A+B)/2
and 
A+B-C=3 pi implies A+B =3 pi + C, so 
cos[(A+B)/2] = cos [3 pi/2  + C/2]
and  with the equivalence cos (3Pi/2  + X) = sinX

sinA+sinB-sinC =  cos(C/2)+ sin(C/2) 
You might be interested in
-8=-(x+4) what is the answer
Tems11 [23]
Step 1: Flip the equation.
−
x
+
4
=
−
8
Step 2: Subtract 4 from both sides.
−
x
+
4
−
4
=
−
8
−
4
−
x
=
−
12
Step 3: Divide both sides by -1.
−
x
−
1
=
−
12
−
1
x
=
12
Answer:
x
=
12
5 0
3 years ago
Find the greatest common factor of 24 and 45.
Anit [1.1K]
3.

3x15=45
3x8=24.
Hope I helped!
5 0
3 years ago
Read 2 more answers
Jane needs $20 to buy her radio. She has saved $15.
UNO [17]

Answer: i think it's 75

Step-by-step explanation: because 5 is half of 10 and 10 is half it makes 75

5 0
2 years ago
A suitcase measures 24 inches long and 18 inches high, what is the diagonal length of the suitcase?
pickupchik [31]

Answer:

The diagonal is 30 inches

Step-by-step explanation:

Assuming a rectangular suitcase (with right angles), we can use the Pythagorean theorem to solve this

a² + b² = c²

so we plug our two values to find the diagonal (hypotenuse)

24² + 18² = c²

576 + 324 = c²

900 = c²

c = √900

c = 30

The diagonal is 30 inches

5 0
3 years ago
Read 2 more answers
The Johnson twins were born five years after their older sister. This​ year, the product of the three​ siblings' ages is exactly
Mamont248 [21]

Answer:

13 years.

Step-by-step explanation:

Suppose, today, the Johnson twins' age is x years. Then the age of their elder sister will be (x + 5) years old. It is given that product of the three​ siblings' ages is exactly 2998 more than the sum of their ages. Therefore:

x + x + x + 5 + 2998 = (x)(x)(x + 5).

3x + 3003 = x^3 + 5x^2.

x^3 + 5x^2 - 3x - 3003 = 0.

To solve the question, factor theorem will be used. It states if any number c satisfies the equation f(c) = 0, then c is the factor of f(x). By observation, it can be seen that x = 13 can be a possible candidate for the factor of f(x). To verify, check f(13).

f(13) = 13^3 + 5(13^2) - 3(13) - 3003 = 2197 + 845 - 39 - 3003 = 0.

Since f(13) = 0, therefore x = 13 is the factor of f(x).

Now applying synthetic division:

Column 1       2       3       4            5

     13    |         1       5      -3        -3003  (Row 1)

______|______<u>  _13__234___3003</u>   (Row 2)

            |         1       18      231          0    (Row 3)

The method requires to write the coefficients of all the powers in the Row 1 on the right hand side of the table. Put the factor x = 13 on the left hand side of the table (Row 1 Column 1). The first step involves the second column elements to be added. Since there is only 1, thus there will be 1 below the line. Next step involves multiplying 1 with the factor (which is 13) and this will be the element for row 2 column 3. The add the elements of the column 3. The answer comes out to be -3. Repeat the above steps for the columns 4 and 5. The sum of the column 5 (the last column) should be 0, which is the case. The elements of the last row are actually the coefficients of the quadratic equation which is resultant from dividing f(x) by (x - 13). Thus:

x^2 + 18x + 231 = 0.

Using completing the square:

x^2 + 18 = -231.

(x)^2 + 2*(x)*(9) + (9)^2 = -231 + (9)^2.

(x + 9)^2 = -231 + 81.

(x + 9)^2 = -150.

Taking square root on both sides shows that rest of the 2 answers of this polynomial will be complex roots since square root of -150 does not exist in real numbers. Therefore, since the age is a real quantity and not a complex quantity, the age of the twins is 13 years!!!

8 0
3 years ago
Other questions:
  • The admission fee at an amusement park is $2.00 for children and $5.60 for adults. On a certain day, 352 people entered the park
    9·1 answer
  • Can a function have a vertical and horizontal asymptote
    5·1 answer
  • The last time David filled up his truck with gas, he paid $27.44 for 7 gallons. This time, he needs 15 gallons. If the price is
    10·1 answer
  • THIS IS A MULTI CHOICE ANSWER
    10·1 answer
  • the cost of a pen is 3 times the cost of a pencil and cost of a notebooks is four times that of a pen. If the cost of 6 pencils,
    6·2 answers
  • What is the approximate value of x in the triangle below
    9·1 answer
  • By visual inspection, determine the best-fitting regression model for the<br><br> scatterplot.
    7·1 answer
  • An elevator is on the twelfth floor it goes down 11 floors and than up 5 floors what floor is the elevator on now
    13·2 answers
  • Plssss help meee I need help
    7·1 answer
  • Ajar contains 100 coins. If it is very unlikely that you will randomly choose a quarter out of the jar, how many quarters
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!