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
brilliants [131]
2 years ago
8

Write the trigonometric expression sin(sin−1u−tan−1v) as an algebraic expression in u and v. Assume that the variables u and v r

epresent positive real numbers.
Mathematics
1 answer:
igomit [66]2 years ago
8 0

Answer:

[u – v√(1 – u²)]/√(1 + v²)

Step-by-step explanation:

Let sin^-1(u) = A, therefore sinA = u.

We know that sin(theta) = opposite/hypothenuse

Therefore, sinA = u/1 and u is the opposite side to angle A while 1 is the hypotenuse. Draw an acute triangle placing u opposite to angle A and 1 as the hypotenuse. By Pythagoras theorem the adjacent would be √(1 – u²).

By doing this, it means cosA = adjacent/hypotenuse = √(1 – u²)/1 = √(1 – u²)

Also, let tan^-1(v) = B, therefore tanB = v.

We know that tan(theta) = opposite/adjacent

Therefore, tanB = v/1 and v is the opposite side to angle B while 1 is the adjacent. Draw an acute triangle placing v opposite to angle B and 1 as the adjacent. By Pythagoras theorem the hypothenuse would be √(1 + v²).

Therefore, sinB = opposite/hypotenuse = v/√(1 + v²) and cosB = adjacent/hypotenuse = 1/√(1 + v²)

Now,

sin[sin^–1(u) – tan^–1(v)] =

sin(A – B) =

sinAcosB – sinBcosA =

u[1/√(1 + v²)] – [v/√(1 + v²)][√(1 – u²)] =

[u/√(1 + v²)] – [v√(1 – u²)/√1 + v²)] =

[u – v√(1 – u²)]/√(1 + v²).

You might be interested in
The boeing 747 airplane is 250 feet in length. If a model of this plane is 8 inches long , what scale was used to create this mo
cluponka [151]

Answer: The wingspan is 36 m.

Using a proportion to solve this, we write the scale factor as a ratio first:  19/38, since 19 is the size of the model's length and 38 is the real length.  For the second ratio, we have 18 for the size of the model wingspan and x for the real wingspan:

19/38 = 18/x

Cross multiply:

19*x = 38*18

19x = 684

8 0
3 years ago
Please can anyone help me please​
Step2247 [10]
4.5, 4, 3.5, 3, 2.5, 2 and use the pencil and ruler, love a bit of MathsWatch
7 0
3 years ago
Read 2 more answers
Can u pls help me with this question
ziro4ka [17]

Step-by-step explanation:

I am not sure bout this question sry

you reap what you sow ;)

6 0
2 years ago
What is the value of the expression 14 + 6 • 2 – 10 ÷ 5?
Alex777 [14]
D 24 do order of operations perenthesis, exponents, multiplication or division, addition or subtraction

7 0
3 years ago
Pleas help I’m so lost
Svetradugi [14.3K]
Its the middle two. Hope I helped
5 0
3 years ago
Other questions:
  • A store manager ordered 402 baseball caps and 122 ski caps estimate the total number of caps the manager ordered
    6·1 answer
  • PLEASE ANSWER QUICKLY ASAP <br>ANSWER QUESTION A AND B​
    7·1 answer
  • Use simple interest to find the interest and ending balance
    9·1 answer
  • What is the solution to this system of equations 3x+y=17 and x+2y=49
    13·1 answer
  • HELP ASAP WILL MARK BRAINLIEST
    7·1 answer
  • Help, what are the next three numbers??
    14·2 answers
  • Janie ordered boxed lunches for a student advisory committee meeting. Each lunch costs $4. The total cost of the lunches is $47,
    9·2 answers
  • Anlatarak cozmicekseniz cevaplamayin:) ​
    15·1 answer
  • Question 4 (1 point)
    9·1 answer
  • Incorrect
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!