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
HELP ME WITH THIS PLEASE!!!!
Vlada [557]

The answer is left two places.

For example 5.% would be 0.05 as a decimal.

5 0
3 years ago
Last night, the two dinner specials at Henry's favorite restaurant were salmon filet and steak. The restaurant served 55 special
sergeinik [125]
Since 11 out of 55 specials were salmon filet,

The percentage of specials that were salmon filet is 11/55 = 20/100 = 20%.
7 0
3 years ago
Read 2 more answers
Given an equation x3 - 8x2 - 9x + 72 = 0, find the zeros.
sveta [45]

Answer:

= 28/3

Step-by-step explanation:

Let's solve your equation step-by-step.

x(3)−(8)(2)−9x+72=0

Step 1: Simplify both sides of the equation.

x(3)−(8)(2)−9x+72=0

3x+−16+−9x+72=0

(3x+−9x)+(−16+72)=0(Combine Like Terms)

−6x+56=0

−6x+56=0

Step 2: Subtract 56 from both sides.

−6x+56−56=0−56

−6x=−56

Step 3: Divide both sides by -6.

−6x

−6

=

−56

−6

x=

28

3

Answer:

x=

28

3

7 0
3 years ago
Maya has 120 caramel apples to sell. Each caramel apple is covered with one toppin.
EleoNora [17]

they got sold by her

Step-by-step explanation:

lol she sold her apples to people

5 0
3 years ago
At what value of x does the graph of the following function F(x) have a
tankabanditka [31]

Given:

The function is

F(x)=\dfrac{1}{x+2}

To find:

The vertical asymptote of the given function.

Solution:

Vertical asymptote are the vertical line passes thought the values for which the function is not defined.

To find the vertical asymptote, equate the denominator equal to 0.

We have,

F(x)=\dfrac{1}{x+2}

Denominator is (x+2).

x+2=0

x=-2

The vertical asymptote is x=-2.

Therefore, the correct option is B.

8 0
2 years ago
Read 2 more answers
Other questions:
  •   Evaluate the function rule for the given value. for x = –2   –24
    7·2 answers
  • Two friends share 7 cookies equally how many does each friend get
    15·2 answers
  • A surveying firm bought a GPS system for
    8·1 answer
  • 4193 times 381 (with work)
    11·2 answers
  • Mara and Taylor need to rent a car for 6 days. If the cost of the car is $105 for each day, which of the following expressions c
    10·1 answer
  • How do you convert meters per second to miles per hour?
    6·1 answer
  • School band sold 30 raffle tickets each ticket is labeled with a number 1 to 31 winning ticket will be drawn what is the probabi
    7·1 answer
  • Amanda found the equation 10x+5y=20 in the “linear equations” chapter of her math book.
    10·1 answer
  • Which product is positive?<br> I NEED THE ANSWER ASAP
    14·2 answers
  • Isabella’s mom takes her and two other friends mini-golfing. The table below shows how much different things cost at the mini-go
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!