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
kiruha [24]
2 years ago
13

Find the EXACT value of sin(A−B) if cos A = 3/5 where A is in Quadrant IV and cos B = 12/13 where B is in Quadrant IV. Assume al

l angles are measured from standard position. sin(A−B) =
Mathematics
1 answer:
MissTica2 years ago
4 0

\bf \textit{Sum and Difference Identities} \\\\ sin(\alpha - \beta)=sin(\alpha)cos(\beta)- cos(\alpha)sin(\beta)

well, for both angles A and B we're on the IV Quadrant, meaning, the sine is negative, the cosine is positive, likewise, the opposite side is negative and the adjacent side for the angle is positive.

\bf cos(A)=\cfrac{\stackrel{adjacent}{3}}{\underset{hypotenuse}{5}}\qquad \qquad \stackrel{\textit{getting the opposite side}}{b=\pm\sqrt{5^2-3^2}}\implies b = \pm 4 \\\\\\ \stackrel{IV~Quadrant}{b = -4}\qquad \qquad sin(A)=\cfrac{\stackrel{opposite}{-4}}{\underset{hypotenuse}{5}} \\\\[-0.35em] ~\dotfill\\\\ cos(B)=\cfrac{\stackrel{adjacent}{12}}{\underset{hypotenuse}{13}}\qquad \qquad \stackrel{\textit{getting the opposite side}}{b=\pm\sqrt{13^2-12^2}}\implies b = \pm 5

\bf \stackrel{IV~Quadrant}{b = -5}\qquad \qquad sin(B)=\cfrac{\stackrel{opposite}{-5}}{\underset{hypotenuse}{13}} \\\\[-0.35em] ~\dotfill\\\\ sin(A-B)=\cfrac{-4}{5}\cdot \cfrac{12}{13}-\left( \cfrac{3}{5}\cdot \cfrac{-5}{13} \right)\implies sin(A-B)=\cfrac{-48}{65} - \left( \cfrac{-15}{65} \right) \\\\\\ sin(A-B)=\cfrac{-48}{65} + \cfrac{15}{65}\implies sin(A-B)=\cfrac{-33}{65}

You might be interested in
What is the solution to the system of equations? y=3x+1 y=-2x-4
BabaBlast [244]

Answer:

(-1,-2)

Step-by-step explanation:

The solution is where the two lines intersect

The graphs intersect at x=-1, y=-2

(-1,-2)

8 0
3 years ago
Read 2 more answers
Yash brought apples and bananas to a picnic The number of apples was three more than twice the number of beane Tach brought 11 a
Ivenika [448]

Answer:

25 bananas

Step-by-step explanation:

11 apples doubled is 22 then plus 3 in 25 this he brought 25 bananas

7 0
3 years ago
PLZ HELP QUICK I NEED TO TURN THIS IN ;Twice a number is fourteen. Write and solve an equation to nd the number of miles that mu
LuckyWell [14K]
2n=14 n being the “number” divide 2 on both sides and you’re left w n=14/2 or7
5 0
3 years ago
How to solve -5y-y=1
goldenfox [79]
Since both y’s are negative you can combine them to make -6y=1 then you divide -6 on each Side to get y=6
5 0
2 years ago
Read 2 more answers
At maximum speed, an airplane travels 2,400 miles against the wind in 6 hours. Flying with the wind, the plane can travel the sa
Hatshy [7]
X - y  = 2400/6 = 400        where x = speed of plane and y = speed of wind.

x + y =  2400/5 = 480          - flying with the wind

adding the 2 equations 
2x = 880
x = 440

Speed of the plane with no wind = 440 mph
5 0
3 years ago
Read 2 more answers
Other questions:
  • The ratio of the number of Jackie's pink T-shirts to the number of her purple T-shirts is 4:3. Which of the following cannot be
    8·2 answers
  • La longitud de 36.27? Porfavor
    10·1 answer
  • The total amount of silver produced in the world in 2015 was 886.7 million ounces. What percent was produced by the United State
    10·1 answer
  • Can a equilateral triangle can be scalene
    15·2 answers
  • If 50 milliliters of a liquid are poured from a graduated cylinder into a container with a different shape, how much liquid will
    6·1 answer
  • (Need help asap) A company has 10,000 employees that work at 6 different locations. The company wants to determine the number of
    9·1 answer
  • John walked from town A to Town B at a uniform speed of 4km/hr.When he reached town B ,he was turned back immediately and he wal
    8·2 answers
  • Solving a word problem with two unknowns using a linear equation
    6·1 answer
  • Can anyone help me with this Midterm Advanced Algebra problem. (DONT ANSWER IF YOUR NOT SURE)
    12·1 answer
  • What is the only way to increase power of a significance test when lowering the probability of committing a Type I error
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!