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
Temka [501]
3 years ago
12

Trigonometry help!! - double angle formulae

Mathematics
1 answer:
ivolga24 [154]3 years ago
8 0

Answer:

The two rules we need to use are:

Sin(a + b) = sin(a)*cos(b) + sin(b)*cos(a)

cos(a + b) = cos(a)*cos(b) - sin(a)*sin(b)

And we also know that:

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

To solve the relations, we start with the left side and try to construct the right side.

a) Sin(3*A) = sin (2*A + A) = sin(2*A)*cos(A) + sin(A)*cos(2*A)

sin(A + A)*cos(A) + sin(A)*cos(A + A)

(sin(A)*cos(A) + sin(A)*cos(A))*cos(A) + sin(A)*(cos(A)*cos(A) - sin(A)*sin(A))

sin(A)*cos^2(A) + sin(A)*cos^2(A) + sin(A)*cos^2(A) - sin^3(A)

3*sin(A)*cos^2(A) - sin(A)*sin^2(A)

sin(A)*(3*cos^2(A) - sin^2(A))

Now we can add and subtract 4*sin^3(A)

sin(A)*(3*cos^2(A) - sin^2(A)) + 4*sin^3(A) -  4*sin^3(A)

sin(A)*(3*cos^2(A) + 3*sin^2(A)) - 4*sin^3(A)

sin(A)*3*(cos^2(A) + sin^2(A)) - 4*sin^3(A)

3*sin(A) - 4*sin^3(A)

b) Here we do the same as before:

cos(3*A) = 4*cos^3(A) - 3*cos(A)

We start with:

Cos(2*A + A) =  cos(2*A)*cos(A) - sin(2*A)*sin(A)

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

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

= (cos^2(A) - sin^2(A))*cos(A) - sin^2(A)*cos(A) - sin^2(A)*cos(A)

= cos^3(A) - 3*sin^2(A)*cos(A)

=  cos(A)*(cos^2(A) - 3*sin^2(A))

now we subtract and add 4*cos^3(A)

= cos(A)*(cos^2(A) - 3*sin^2(A)) + 4*cos^3(A) - 4*cos^3(A)

= cos(A)*(-3*cos^2(A) - 3*sin^2(A)) + 4*cos^3(A)

= cos(A)*(-3)*(cos^2(A) + sin^2(A)) + 4*cos^3(A)

= -3*cos(A) + 4*cos^3(A)

You might be interested in
An airplane travels 2416 kilometers against the wind in 4 hours and 2896 kilometers with the wind in the same amount of time. Wh
oee [108]

Answer: the rate of the plane in still air is 664 km/h and the rate of the wind is 60 km/h

Step-by-step explanation:

Let x represent the rate of the plane in calm air.

Let y represent the rate of the wind.

An airplane travels 2416 kilometers against the wind in 4 hours. This means that the total speed with which the plane flew is (x - y) mph.

Distance = speed × time

Distance travelled by the plane while flying against the wind is

2416 = 4(x - y)

Dividing both sides of the equation by 4, it becomes

604 = x + y- - - - - - - - - - - 1

It flew 2896 kilometers with the wind in the same amount of time.. This means that the total speed with which the plane flew with the wind is (x + y) mph.

Distance travelled by the plane while flying with the wind is

2896 = 4(x + y)

Dividing both sides of the equation by 2, it becomes

724 = x + y- - - - - - - - - - - 2

Adding equation 1 to equation 2, it becomes

1328 = 2x

x = 1328/2

x = 664

Substituting x = 664 into equation 2, it becomes

724 = 664 + y

y = 724 - 664

y = 60

5 0
3 years ago
All help is appreciated. Find m
Annette [7]

Answer:

B.) 73°

Step-by-step explanation:

To find m<A, first you must find it's supplementary angle. In order to do this, you must determine the missing interior angle. We'll call the missing angle x

A pentagon has 540°. Add up the known angles.

96°+118°+115°+104°+x = 540°

433°+x = 540°

x = 107°

Now that we know the value of x, we can find the m<A. Supplementary angles are two angles that add up to 180°, which is a flat line. We can see in the diagram that m<a + 107° is a flat line, meaning m<a + 107° = 180°

Solve accordingly.

m<a + 107° = 180°

m<a = 73°

3 0
3 years ago
Read 2 more answers
Classify each function as a power function, root function, polynomial (state its degree), rational function, algebraic function,
Gnoma [55]

x=0-87 hope this helps

5 0
2 years ago
3/7 / 3 in simplest form
vovangra [49]

Answer:

3/7^3

Mark Brainliest

3 0
2 years ago
Read 2 more answers
Graph the second equation to find the solution of the system of equations.
dsp73
Answer: (-2,2)

Explanation: I plugged it into a graphing calc!

3 0
3 years ago
Read 2 more answers
Other questions:
  • 15 POINTS !!
    11·2 answers
  • What is the circumference of the blue circle?
    7·1 answer
  • Find the ratio of the width to the length of the rectangle, then simplify the ratio. Use the conversion 100 cm = 1 m.
    8·1 answer
  • If it takes six men six days to dig six holes, how long will it take one man to dig half a hole?
    5·1 answer
  • NVM...........................................................................
    6·2 answers
  • What is the slope of the line that passes through the pair of points (1/3, -1) and ( -2, 9/2)​
    15·2 answers
  • Which equation is a true proportion?
    15·2 answers
  • 13 less than fourteen times a certain number is twenty-nine more than 7 times that number. What is the number? (I only need the
    6·1 answer
  • Luis and Erin are playing a game. They each start with 0 points.At the end of the game, Luis has 250 points, and Erin has
    12·1 answer
  • Given the equation: x^2+6x+8=0
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!