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
JulijaS [17]
3 years ago
11

Please solve the following sum or difference identity.

Mathematics
2 answers:
xxTIMURxx [149]3 years ago
6 0

Answer:

sin(A - B) = \frac{4}{5}

Step-by-step explanation:

Given:

sin(A) = \frac{24}{25}

sin(B) = -\frac{4}{5}

Need:

sin(A - B)

First, let's look at the identities:

sum: sin(A + B) = sinAcosB + cosAsinB

difference: sin(A - B) = sinAcosB - cosAsinB

The question asks to find sin(A - B); therefore, we need to use the difference identity.

Based on the given information (value and quadrant), we can draw reference triangles to find the simplified values of A and B.

sin(A) = \frac{24}{25}

cos(A) = \frac{7}{25}

sin(B) = -\frac{4}{5}

cos(B) = \frac{3}{5}

Plug these values into the difference identity formula.

sin(A - B) = sinAcosB - cosAsinB

sin(A - B) = (\frac{24}{25})(\frac{3}{5}) - (-\frac{4}{5})(\frac{7}{25})

Multiply.

sin(A - B) = (\frac{72}{125}) + (\frac{28}{125})

Add.

sin(A - B) = \frac{4}{5}

This is your answer.

Hope this helps!

muminat3 years ago
5 0

GIVEN:

sinA = 24/25

sinB = - 4/5

IDENTITIES:

  • sin(A + B) = sinAcosB + cosAsinB
  • sin(A - B) = sinAcosB - cosAsinB

ANSWER:

We have find the unknown trigo ratio by constructing a given right angled triangle using trigonometric function.

  • cosA = 7/25 & cosB = 3/5

We know the identity of difference, so we have to just plug the respective value.

sin(A - B) = sinAcosB - cosAsinB

  • (24/25 × 3/5) - (7/25 × - 4/5)
  • 72/125 - (- 28/125)
  • 72/125 + 28/125
  • 100/125 = 4/5.

Hence, sin(A - B) = 4/5.

You might be interested in
Let f(x) = 12/4x+2 Find f(-1). (1 point)
noname [10]

Answer:

-1

Step-by-step explanation:

let,x=-1

f(x)= 12/4x + 2

f(-1)= 12/4x(-1) + 2

=12/(-4) +2

= -3+2

= -1

3 0
3 years ago
A boat costs $12,050 and decreases in value by 12% per year. How much will the boat be worth after 9 years?
Anvisha [2.4K]
Hi there
The formula is
A=p (1-r)^t
A future value?
P present value 12050
R rate of decreases 0.12
T time 9 years
A=12,050×(1−0.12)^(9)
A=3,813.6 round your answer
A=3814

Hope it helps
4 0
4 years ago
What’s 1/4+1/3 equal
Pani-rosa [81]

Answer:

7/12

Step-by-step explanation:

1/4 +1/3

We need to get a common denominator of 12

1/4*3/3 = 3/12

1/3 *4/4 = 4/12

3/12+4/12 = 7/12

5 0
3 years ago
Read 2 more answers
From a 200-ton pile of coal, a conveyor belt removes
likoan [24]

Answer:

56 min

Step-by-step explanation:

8 0
3 years ago
Jonathan wants to make mashed potatoes for eight people. He found a recipe which feeds two people and requires five ounces of po
galben [10]

Answer:

2lb 32 oz.

Step-by-step explanation:

because 2=5 so 8=32  

32 divided by 2 =16 so 32 oz  2lb

4 0
3 years ago
Other questions:
  • Solve the literal equation cy−7=5d+3ycy−7=5d+3y for yy.
    14·1 answer
  • NEED HELP ASAP WILL GIVE BRAINLY IF CORRECT 20 POINTS
    7·2 answers
  • Parallelogram F C D E is shown. Sides D C and F E are parallel, and sides F C and E D are parallel. The length of C D is 4 r + 1
    7·2 answers
  • To practice for a competition, Jenna swam 680 meters in the pool each day for 3 weeks. How many kilometers did Jenna swim in tho
    9·1 answer
  • Jacque needs to buy some pizzas for a party at her office. She's ordering from a restaurant that charges a $7.50, 7, point, 50 d
    11·1 answer
  • Pls answer this tyyyyy
    9·1 answer
  • Wallace bought 4 gallons of milk last week because his family drinks a lot of milk. If
    12·1 answer
  • Simplify this problem
    9·2 answers
  • Tell me about your previous experiences with math. Your experiences can be positive or negative.
    6·1 answer
  • There are 750 students in my middle
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!