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
pickupchik [31]
3 years ago
12

PLZ HELP!!! I Will give brainliest. What is the value of x in sin(3x)=cos(6x) if x is in the interval of 0≤x≤π/2

Mathematics
1 answer:
sertanlavr [38]3 years ago
5 0

Answer:

sin(2x)=cos(π2−2x)

So:

cos(π2−2x)=cos(3x)

Now we know that cos(x)=cos(±x) because cosine is an even function. So we see that

(π2−2x)=±3x

i)

π2=5x

x=π10

ii)

π2=−x

x=−π2

Similarly, sin(2x)=sin(2x−2π)=cos(π2−2x−2π)

So we see that

(π2−2x−2π)=±3x

iii)

π2−2π=5x

x=−310π

iv)

π2−2π=−x

x=2π−π2=32π

Finally, we note that the solutions must repeat every 2π because the original functions each repeat every 2π. (The sine function has period π so it has completed exactly two periods over an interval of length 2π. The cosine has period 23π so it has completed exactly three periods over an interval of length 2π. Hence, both functions repeat every 2π2π2π so every solution will repeat every 2π.)

So we get ∀n∈N

i) x=π10+2πn

ii) x=−π2+2πn

iii) x=−310π+2πn

(Note that solution (iv) is redundant since 32π+2πn=−π2+2π(n+1).)

So we conclude that there are really three solutions and then the periodic extensions of those three solutions.

5.8K views

View upvotes

5

Related Questions (More Answers Below)

You might be interested in
If you help me with this fast I will brain you.<br> Thanks.
irakobra [83]

Answer:

-2 and -6 is the correct answer

5 0
3 years ago
Help me plzzzzzzzzzzzzzzzzzzz
Shkiper50 [21]

Answer:

5^8/5^6=5^2

Step-by-step explanation:

When dividing numbers with powers, it is handy to remember that

x^y/x^z=x^y^-^z

so

5^8/5^6=5^8^-^6 = 5^2

4 0
3 years ago
Read 2 more answers
Jayana is trying to run a certain number of miles by the end of the month. If Jayana is 30% of the way to achieving her goal and
torisob [31]
Jayana is trying to run 30 miles by the end of the months.

30% / 100% = 9 / x

9 * 100 = 900

900 / 30 = 30 miles
4 0
3 years ago
if you deposit $10000 at 11%(simple interest), how long will it be until the total amount in the account is $21000?
ki77a [65]

10000:100*11=1100  income per year

21000-10000=11000 need to have income

11000:1100=10 years will pass time

4 0
3 years ago
Find the amount of 30000 naira 5 and half years at 7%​
Nataly_w [17]

Answer:41550

Step-by-step explanation:

30000×.07=2100

2100×5.5=11550

11550+30000=41550

5 0
3 years ago
Other questions:
  • Consider Akelia’s sequence 5, 8, 11, 14, 17, ….
    9·1 answer
  • Write the number 1/10,000,000 as a power of 10 using a negative exponents
    5·1 answer
  • Determine whether the series is convergent or divergent. 1 2 3 4 1 8 3 16 1 32 3 64 convergent divergent Correct:
    14·1 answer
  • A fish tank has a length of 14cm, a width of 25cm, and a height of 15cm. It is only filled with water up to a height of 7 centim
    15·1 answer
  • The cost of renting the party room at a restaurant is $50.00. Snacks cost $13.50 per person. Write an expression to describe the
    7·1 answer
  • What are the coordinates of the endpoints of the segment
    14·2 answers
  • Helpppppppp meeeeeeeeeeee
    15·1 answer
  • What is the colon form? :)​
    7·1 answer
  • there are approximately 3 million births in the unitad states each year .find the birth rate per minute
    15·2 answers
  • What is the solution to this matrix equation?[ -1 4 3 2] [x y] = [-26 8] i need to find (x=?) and (y=?)
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!