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
bixtya [17]
3 years ago
14

If A and B are two angles in standard position in Quadrant I, find cos( A +B ) for the given function values. sin A = 8/17 and c

os B = 12/13
-220/221
-140/221
140/221
220/221

If A and B are two angles in standard position in Quadrant I, find cos( A -B ) for the given function values. sin A = 3/5 and cos B= 12/37
153/185
57/185
-57/185
-153/185

If A and B are two angles in standard position in Quadrant I, find cos( A - B) for the given function values.
sin A = 15/17 and cos = 3/5
-84/85
-36/85
36/85
84/85

If A and B are two angles in standard position in Quadrant I, find cos( A + B) for the given function values.
sin A = 15/17 and cos = 3/5
-220/221
-140/221
140/221
220/221

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 = 5/13
-33/65
33/65
-63/65
63/65

If A and B are two angles in standard position in Quadrant I, find cos( A + B) for the given function values.
sin A = 3/5 and cos = 12/37
153/185
57/185
-57/185
-153/185
Mathematics
1 answer:
horsena [70]3 years ago
4 0

Answer:

Part 1) cos(A + B) = \frac{140}{221}

Part 2) cos(A - B) = \frac{153}{185}

Part 3) cos(A - B) = \frac{84}{85}

Part 4) cos(A + B) = -\frac{36}{85}

Part 5) cos(A - B) = \frac{63}{65}

Part 6) cos(A+ B) = -\frac{57}{185}

Step-by-step explanation:

<u><em>the complete answer in the attached document</em></u>

Part 1) we have

sin(A)=\frac{8}{17}

cos(B)=\frac{12}{13}

Determine cos (A+B)

we know that

cos(A + B) = cos(A) cos(B)-sin(A) sin(B)

step 1

Find the value of cos(A)

Remember that

cos^2(A)+sin^2(A)=1

substitute the given value

cos^2(A)+(\frac{8}{17})^2=1

cos^2(A)+\frac{64}{289}=1

cos^2(A)=1-\frac{64}{289}

cos^2(A)=\frac{225}{289}

cos(A)=\pm\frac{15}{17}

The angle A belong to the I quadrant, the cosine is positive

cos(A)=\frac{15}{17}

step 2

Find the value of sin(B)

Remember that

cos^2(B)+sin^2(B)=1

substitute the given value

sin^2(B)+(\frac{12}{13})^2=1

sin^2(B)+\frac{144}{169}=1

sin^2(B)=1-\frac{144}{169}

sin^2(B)=\frac{25}{169}

sin(B)=\pm\frac{25}{169}

The angle B belong to the I quadrant, the sine is positive

sin(B)=\frac{5}{13}

step 3

Find cos(A+B)

substitute in the formula

cos(A + B) = \frac{15}{17} \frac{12}{13}-\frac{8}{17}\frac{5}{13}

cos(A + B) = \frac{180}{221}-\frac{40}{221}

cos(A + B) = \frac{140}{221}

Part 2) we have

sin(A)=\frac{3}{5}

cos(B)=\frac{12}{37}

Determine cos (A-B)

we know that

cos(A - B) = cos(A) cos(B)+sin(A) sin(B)

step 1

Find the value of cos(A)

Remember that

cos^2(A)+sin^2(A)=1

substitute the given value

cos^2(A)+(\frac{3}{5})^2=1

cos^2(A)+\frac{9}{25}=1

cos^2(A)=1-\frac{9}{25}

cos^2(A)=\frac{16}{25}

cos(A)=\pm\frac{4}{5}

The angle A belong to the I quadrant, the cosine is positive

cos(A)=\frac{4}{5}

step 2

Find the value of sin(B)

Remember that

cos^2(B)+sin^2(B)=1

substitute the given value

sin^2(B)+(\frac{12}{37})^2=1

sin^2(B)+\frac{144}{1,369}=1

sin^2(B)=1-\frac{144}{1,369}

sin^2(B)=\frac{1,225}{1,369}

sin(B)=\pm\frac{35}{37}

The angle B belong to the I quadrant, the sine is positive

sin(B)=\frac{35}{37}

step 3

Find cos(A-B)

substitute in the formula

cos(A - B) = \frac{4}{5} \frac{12}{37}+\frac{3}{5} \frac{35}{37}

cos(A - B) = \frac{48}{185}+\frac{105}{185}

cos(A - B) = \frac{153}{185}

Part 3) we have

sin(A)=\frac{15}{17}

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

Determine cos (A-B)

we know that

cos(A - B) = cos(A) cos(B)+sin(A) sin(B)

step 1

Find the value of cos(A)

Remember that

cos^2(A)+sin^2(A)=1

substitute the given value

cos^2(A)+(\frac{15}{17})^2=1

cos^2(A)+\frac{225}{289}=1

cos^2(A)=1-\frac{225}{289}

cos^2(A)=\frac{64}{289}

cos(A)=\pm\frac{8}{17}

The angle A belong to the I quadrant, the cosine is positive

cos(A)=\frac{8}{17}

step 2

Find the value of sin(B)

Remember that

cos^2(B)+sin^2(B)=1

substitute the given value

sin^2(B)+(\frac{3}{5})^2=1

sin^2(B)+\frac{9}{25}=1

sin^2(B)=1-\frac{9}{25}

sin^2(B)=\frac{16}{25}

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

The angle B belong to the I quadrant, the sine is positive

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

step 3

Find cos(A-B)

substitute in the formula

cos(A - B) = \frac{8}{17} \frac{3}{5}+\frac{15}{17} \frac{4}{5}

cos(A - B) = \frac{24}{85}+\frac{60}{85}

cos(A - B) = \frac{84}{85}

Part 4) we have

sin(A)=\frac{15}{17}        

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

Determine cos (A+B)

we know that    

cos(A + B) = cos(A) cos(B)-sin(A) sin(B)

step 1

Find the value of cos(A)

Remember that

cos^2(A)+sin^2(A)=1

substitute the given value

cos^2(A)+(\frac{15}{17})^2=1

cos^2(A)+\frac{225}{289}=1

cos^2(A)=1-\frac{225}{289}      

cos^2(A)=\frac{64}{289}

cos(A)=\pm\frac{8}{17}

The angle A belong to the I quadrant, the cosine is positive

cos(A)=\frac{8}{17}

step 2

Find the value of sin(B)

Remember that

cos^2(B)+sin^2(B)=1

substitute the given value

sin^2(B)+(\frac{3}{5})^2=1

sin^2(B)+\frac{9}{25}=1

sin^2(B)=1-\frac{9}{25}

sin^2(B)=\frac{16}{25}

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

The angle B belong to the I quadrant, the sine is positive

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

step 3

Find cos(A+B)

substitute in the formula    

cos(A + B) = \frac{8}{17} \frac{3}{5}-\frac{15}{17} \frac{4}{5}

cos(A + B) = \frac{24}{85}-\frac{60}{85}

cos(A + B) = -\frac{36}{85}

Download odt
You might be interested in
The angle of rotation at which point A’ coincidences point
anygoal [31]

Answer:

216 degrees

Step-by-step explanation:

Given that ABCDE is a regular pentagon.

Hence each angle would equal = {2(5)-4}/5 right angles

=6(90)/5 =108 degrees

Since regular pentagon rotation will not disturb the shape.

When counterclockwise rotated, if 108 degrees rotated A would become E.

For another 108 degrees A would come to D

Hence angle required for rotation for A to coincide with D = 2(108)

=216 degrees

8 0
2 years ago
I need help with these................
larisa [96]

Answer:

(5,4)

:))))))))))))))))

3 0
3 years ago
5/6- 2/3= need answer plz
Natalka [10]

Answer:

0.16666666666

Step-by-step explanation:

5 0
2 years ago
Triangle FGH with vertices F(6,6), G(8,8), and H(8,3): (a) Reflection: in the line x = 5 (b) Translation: (x,y)→ (x - 7, y - 9)
irakobra [83]

(a) The vertices after the reflection in the line x = 5 are F'(4,6) , G'(2,8) , H'(2,3) .

and (b) after translation , the vertices are F''(-1,-3) , G'' (1,-1) , H''(1,-6) .

In the question a triangle FGH with vertices F(6,6) , G(8,8) and H(8,3) is given

Part (a)

the rule for reflection of point (x,y) by the line x = p  is

(x,y) → (2×p - x , y)

reflection by the line x = 5 ,

we get

the vertices as

F'(2×5-6,6) = (4,6)

G'(2×5-8,8) = (2,8)

H'(2×5 - 8 ,3) = (2,3)

Part (b)

the rule of translation is given as (x,y)→ (x - 7, y - 9)

So , the vertices after translation are

F''(6-7 , 6-9) = (-1,-3)

G''(8-7,8-9) = (1,-1)

H''(8-7,3-9) = (1,-6)

Therefore , (a) The vertices after the reflection in the line x = 5 are F'(4,6)

G'(2,8) , H'(2,3) .

and (b) after translation , the vertices are F''(-1,-3) , G'' (1,-1) , H''(1,-6) .

Learn more about Translation here

brainly.com/question/3456459

#SPJ1

7 0
1 year ago
What expression is equivalent to 13-(-21)?
Naddik [55]

Answer:

34

Step-by-step explanation:

13-(-21) = 13 + 21 = 34

5 0
3 years ago
Read 2 more answers
Other questions:
  • How do you rewrite equations in slope intercept form ?
    12·1 answer
  • 125.3546 to 1 decimal place
    9·2 answers
  • The probability that an event will occur is 1/8 Which of these best describes the likelihood of the event occurring
    12·1 answer
  • 47 + (-68) - 38 - (-94)
    13·1 answer
  • What is the slope-intercept form of the equation below?<br> 12x + 5y = -10
    15·2 answers
  • Solve this set of equation, using elimination or substitution method.
    15·2 answers
  • Marsha deposited ​$7,000 into a savings account years ago. The simple interest rate is ​4%. How much money did Marsha earn in​ i
    12·2 answers
  • Which of the following are identities? Check all that apply.
    7·1 answer
  • PLZ HELP ME <br> NO LINKS PLZ
    8·1 answer
  • Use the graph to find the cost of 8 shirts
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!