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
patriot [66]
3 years ago
15

If a and b are two angles in standard position in Quadrant I, find cos(a+b) for the given function values. sin a=4/5 and cos b=5

/13
Mathematics
2 answers:
soldier1979 [14.2K]3 years ago
5 0

Answer:

cos(a+b)≈0.507

Step-by-step explanation:

Hi there, in Quadrant I both sine and cosine functions are positive.

This cos (a+b) being a Classical Trigonometrical Identity, the product of the sum between two cosines equals the product of two cosines minus the product of two sines.

But we need to find the value of a and b, so that we can go on. Calculate the arccosine and arcsine function respectively is mandatory

cos(a+b)=cosa*cosb-sena*senb\\ cos(a+b)=cosa*\frac{5}{13} -\frac{4}{5}*senb\\ a=arcsin(\frac{5}{13})\\a=22.61\\b=arccos(\frac{4}{5})\\b=36.86\\ 5/13=0.38\\4/5=0.8\\cos(a+b)=cos(22.61)*cos(36.86) -sen(22.61)*sen(36.86)\\ cos (a+b)=0.507

vladimir1956 [14]3 years ago
4 0
First let's find the angles a and b.

 We have then:
 sin a = 4/5
 a = Asin (4/5)
 a = 53.13 degrees.

 cos b = 5/13
 b = Acos5 / 13
 b = 67.38 degrees.

 We now calculate cos (a + b). To do this, we replace the previously found values:
 cos ((53.13) + (67.38)) = - 0.507688738
 Answer: 
 -0.507688738
 Note: there is another way to solve the problem using trigonometric identities.
You might be interested in
Will mark BRAINLIEST
Readme [11.4K]

Answer:

the star is quadrant 2

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
A gym allows members to attend two free strength-building classes each month as part of their $40 monthly membership fee. If the
MariettaO [177]

Answer:

m = 10

Step-by-step explanation:

fjfnbwdhw she djb2dh2bdub2jdb3udje <<< just for filler

6 0
3 years ago
Is it possible for a number to be a rational number that is not an interger but is a whole number. Explain
mylen [45]

Whole numbers are a subset of integers, which in turn are a subset of rational numbers.

So, every whole number is an integer, and every integer is a rational number.

So, it is possible for a rational number not to be an integer. Think of any decimal number: 1.356 is a rational number, but it's not an integer.

On the other hand, if a number is not an integer, it can't be a whole number, because all whole numbers are integers.

5 0
3 years ago
Factor the expression: <br> 30 + 100c
ANEK [815]
10(3+10с)
This expression has a common factor of 10
3 0
3 years ago
You and your friend are using ribbon to make cards. Your ribbon is 78 inch wide. Your friend's ribbon is 58 inch wide. How much
Yakvenalex [24]

Answer:

20 inches longer

Step-by-step explanation:

78-58= 20

4 0
2 years ago
Read 2 more answers
Other questions:
  • Walter is a comic book artist. He usually draws 36 comic panels each day. How many comic panels can he draw in 2 weeks.
    13·2 answers
  • Lena is going to cover her entire garden with topsoil. The garden is 36 feet long by 22 feet wide. A bag of topsoil costs $3 and
    10·1 answer
  • Batting averages in baseball are expressed as decimals to the thousandths place. Antonio gets a hit 1 out of every 3 times at ba
    14·1 answer
  • What is it called when Cupid misses his target?
    11·1 answer
  • Will give lots of points/write a rule to describe each transformation
    14·1 answer
  • In this problem, the tapes used were assumed to be 30.0 m long. Later, when the tapes were standardized, they were found to have
    13·1 answer
  • Please help me- AND PLEASE EXPLAIN
    5·1 answer
  • What is the slope of the line?
    13·1 answer
  • Rachel types
    15·1 answer
  • The graph of quadratic functiong is shown on the grid. The coordinates of the x-intercepts, they-intercept, and the vertex are i
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!