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
mr_godi [17]
3 years ago
6

Given sin(u)= -7/25 and cos(v) = -4/5, what is the exact value of cos(u-v) if both angles are in quadrant 3

Mathematics
1 answer:
solmaris [256]3 years ago
6 0

Given:

\sin (u)=-\dfrac{7}{25}

\cos (v)=-\dfrac{4}{5}

To find:

The exact value of cos(u-v) if both angles are in quadrant 3.

Solution:

In 3rd quadrant, cos and sin both trigonometric ratios are negative.

We have,

\sin (u)=-\dfrac{7}{25}

\cos (v)=-\dfrac{4}{5}

Now,

\cos (u)=-\sqrt{1-\sin^2 (u)}

\cos (u)=-\sqrt{1-(-\dfrac{7}{25})^2}

\cos (u)=-\sqrt{1-\dfrac{49}{625}}

\cos (u)=-\sqrt{\dfrac{625-49}{625}}

On further simplification, we get

\cos (u)=-\sqrt{\dfrac{576}{625}}

\cos (u)=-\dfrac{24}{25}

Similarly,

\sin (v)=-\sqrt{1-\cos^2 (v)}

\sin (v)=-\sqrt{1-(-\dfrac{4}{5})^2}

\sin (v)=-\sqrt{1-\dfrac{16}{25}}

\sin (v)=-\sqrt{\dfrac{25-16}{25}}

\sin (v)=-\sqrt{\dfrac{9}{25}}

\sin (v)=-\dfrac{3}{5}

Now,

\cos (u-v)=\cos u\cos v+\sin u\sin v

\cos (u-v)=\left(-\dfrac{24}{25}\right)\left(-\dfrac{4}{5}\right)+\left(-\dfrac{7}{25}\right)\left(-\dfrac{3}{25}\right)

\cos (u-v)=\dfrac{96}{625}+\dfrac{21}{625}

\cos (u-v)=\dfrac{1 17}{625}

Therefore, the value of cos (u-v) is 0.1872.

You might be interested in
A piece of fabric is in the shape of a triangle as shown below. Find the missing angle measure.​
Ganezh [65]

Answer:

49..................

7 0
3 years ago
On a street, each house has an address between 1000 and 1099, inclusive. at least how many houses are there if at least two of t
notsponge [240]
There are at least 3 houses on a street if at least two of them have addresses that are consecutive integers.
8 0
3 years ago
Simplyfy using appropiate properties 1/4×2/5+-1/6×3/2+3/7×2/5 ​
Triss [41]

Answer:

-1/35

Step-by-step explanation:

* means multiply

because of pemdas you should do three multiplication parts first

(1/4×2/5)+(-1/6×3/2)+(3/7×2/5)

1/20 - 3/12 + 6/35

3/60 - 15/60 + 6/35

-12/60 + 6/35

-1/5 + 6/35

-7/35 + 6/35

-1/35

7 0
3 years ago
Read 2 more answers
The drawing is composed of a rectangle and a semicircle. Find the area of the figure to the nearest unit. Please explain, thank
DanielleElmas [232]
We know that
[area of the figure]=[area of rectangle]+[area of semi circle]

area of rectangle=b*h------> 10*18-----> 180 cm²

area of semicircle=pi*r²/2
diameter=18 cm
radius=18/2----> 9 cm
area of semicircle=pi*9²/2-----> 127.17 cm²

[area of the figure]=[180]+[127.17]------> 307.17 cm²
round <span>to the nearest unit </span>------> 307 cm²

the answer is
the area of the figure is 307 cm²
3 0
3 years ago
Solve. 6−3x=3(8−x) <br> 4 all real numbers −4 no solutions
klio [65]
Yea no solution is your answer
8 0
2 years ago
Other questions:
  • Owen has 12 pieces of rope that are 4 yards each. Owen uses 6 pieces of rope that are each 6 feet long.
    14·1 answer
  • Which of the following qualities does not describe a line? Select all that apply.
    11·2 answers
  • Each of four shelves in a bookcase measures 275 cm. Find the cost of the shelves when the price of lumber is $13.50 per meter.
    5·1 answer
  • Whats 4 squred - 11x + 6 =0
    7·1 answer
  • Help me please! Thanks!
    15·1 answer
  • Find the missing fraction 5/2 =1/3
    12·1 answer
  • Kaylee writes the equation 6x+12=2 (3x+6) can you find the number of solutions this equation has without solving for x​
    15·1 answer
  • in triangle XYZ, XY=15 YZ=8, angle x= (3w-35) and angle y =52 in triangle RST, rs =15, RT=8, angle R=w+17) and S=52 find the ang
    13·1 answer
  • a chemical comapany makes two brands of antifreeze . the first brand is 70% pure antifreeze and the second is 95% pure antifreez
    8·1 answer
  • (b) A private club grew by 7 members each week for 42 weeks. What was the total change in the
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!