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
satela [25.4K]
3 years ago
13

[Pre-Calc]

Mathematics
1 answer:
Simora [160]3 years ago
8 0

<span><span>sin(α+β)</span>=sinαcosβ+cosαsinβ</span>,

and the double angle formula of cosine:

<span><span>cos(2α)</span>=<span>cos2α</span>−<span>sin2α</span>=2<span>cos2α</span>−1=1−2<span>sin2α</span></span>

then:

<span><span>sin(3x)</span>=<span>sin(2x+x)</span>=<span>sin(2x)</span>cosx+<span>cos(2x)</span>sinx=</span>

<span>=<span>(2sinxcosx)</span>⋅cosx+<span>(1−2<span>sin2x</span>)</span>sinx=</span>

<span>=2sinx<span>cos2x</span>+sinx−2<span>sin3x</span>=</span>

<span>=2sinx<span>(1−<span>sin2x</span>)</span>+sinx−2<span>sin3x</span>=</span>

<span>=2sinx−2<span>sin3x</span>+sinx−2<span>sin3x</span>=</span>

<span>=3sinx−4<span>sin3x</span></span>.



<span><span>cos3</span>x</span>
<span>=<span>cos<span>(x+2x)</span></span></span>
<span>=<span>cosx</span><span>cos2</span>x−<span>sinx</span><span>sin2</span>x</span><span> using cos(A+B)=cosAcosB-sinAsinB</span>
<span>=<span>cosx</span><span>(2<span><span>cos^2</span>x</span>−1)</span>−<span>sinx</span><span>(2<span>sinx</span><span>cosx</span>)</span></span><span> using cos2A=2cos^2A-1 and sin2A=2sinAcosA</span>
<span>=2<span><span>cos^3</span>x</span>−<span>cosx</span>−2<span><span>sin^2</span>x</span><span>cosx</span></span> 
<span>=2<span><span>cos^3</span>x</span>−<span>cosx</span>−2<span>(1−<span><span>cos^2</span>x</span>)</span><span>cosx</span></span><span>  using </span><span><span><span>sin^2</span>x</span>+<span><span>cos^2</span>x</span>=1</span>
<span>=2<span><span>cos^3</span>x</span>−<span>cosx</span>−2<span>(<span>cosx</span>−<span><span>cos3^</span>x</span>)</span></span><span> [open the brackets]</span>
<span>=2<span><span>cos^3</span>x</span>−<span>cosx</span>−2<span>cosx</span>+2<span><span>cos^3</span>x</span></span>
<span>=4<span><span>cos^3</span>x</span>−3<span>cosx</span></span><span> [collect terms]</span>



You might be interested in
A function passes through the points (2,9) and (7,34). What are its rate of change and initial value?
Bess [88]

Answer:

The rate of change: 1/5

Initial value: (0,-1)

Step-by-step explanation:

The rate of change is easily 5/25, we just have to simplify it to 1/5.

To get the intial value, just subtract (2,9) by the rate of change twice.

5 0
3 years ago
Find the surface area and volume of the following figures.
Oduvanchick [21]

White figure Area = 128\pi

White surface area = appro. 301

Yellow area = 320\pi

Yellow Surface area = approx. 653

Area found with = 2πrh+2πr2

Surface Area found with = 2πrh+2πr2

You need to memorize them for tests

Hope that helped!!! k

4 0
3 years ago
Read 2 more answers
Help please with this math question
Svetllana [295]
If the new technology innovation improves the production by 10%, they are increasing the amount of cars made by 10%.

Originally, 120 cars were made per day.

10% of 120 is 12.

Since the amount of cars made per day was increased by 12, we can add 12 to 120 to get 132 cars made per day (as the new unit rate).

The question asks how many cars can be produced in 5 days (after the car production increase). We can get the answer by multiplying our new daily amount of cars by 5: 132 times 5.

132 times 5 = 660

So, 660 cars can be produced in the factory in 5 days.
5 0
1 year ago
Two angles are supplementary. The measure of one angle is 54 more than the measure of the other angle. What is the measure of th
il63 [147K]

Answer:

bigger angle is 117°

Step-by-step explanation:

x+x+54= 180 (when two angles are complementary it means that their sum is 180 degrees)

2x+54=180

2x= 180-54

2x=128

x=126/2

x= 63

x1= smaller angle

x1= 63

x2= bigger angle

x2= 63+54

x2=117

4 0
3 years ago
A negative number is ______ a positive number
yawa3891 [41]
A negative number is the inverse of a positive number and a negative number is smaller than a positive  hope this help
5 0
3 years ago
Other questions:
  • there are 5 times as many yellow labs as terriers in the dog park. if there are a total of 18 dogs, how many are terriers
    15·1 answer
  • A number divided by 3 with 19 added equals 36 what is the number
    15·2 answers
  • Evaluate the expression when a = 10.<br> a/4 + 1/3
    9·1 answer
  • What is the difference between -4 and 6?<br>-10<br>-2<br>2<br>10​
    12·2 answers
  • What role does cellular respiration play in the water cycle
    6·1 answer
  • workers are loading boxes onto a truck . So far, they have loaded 48 boxes onto the truck. According to their inventory, they st
    7·1 answer
  • Which is the graph of the parent function f(x) = x2?
    12·1 answer
  • Some number times 7 is equal to the number increased by 9
    15·1 answer
  • What is the constant of proportionality in the equation y=25X?
    15·1 answer
  • Find the missing values in the ratio table. Then write the equivalent ratios. Write each value as a fraction or whole number. Wh
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!