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
NAND"" and ""NOR"" circuits are commonly used as a basis for flash memory chips. A NAND B is defined to be the negation of ""A a
Anit [1.1K]

Answer:

(i) A truth table shows how the truth or falsity of a compound statement depends on the truth or falsity of the simple statements from which it's constructed.

Since A ∧ B (the symbol ∧ means A and B) is true only when both A and B are true, its negation A NAND B is true as long as one of A or B is false.

Since A ∨ B (the symbol ∨ means A or B) is true when one of A or B is true, its negation A NOR B is only true when both A and B are false.

Below are the truth tables for NAND and NOR connectives.

(ii) To show that (A NAND B)∨(A NOR B) is equivalent to (A NAND B) we build the truth table.

Since the last column (A NAND B)∨(A NOR B) is equal to (A NAND B) it follows that the statements are equivalent.

(iii) To show that (A NAND B)∧(A NOR B) is equivalent to (A NOR B) we build the truth table.

Since the last column (A NAND B)∧(A NOR B) is equal to (A NOR B) it follows that the statements are equivalent.

6 0
3 years ago
Help Please.
Vladimir [108]

Answer: total length of frame material is 3.2 meters

Step-by-step explanation:

The perimeter of an object or a plane shape is the distance around the object of plane shape.

Mila plans to frame a poster she bought at a concert. The total length of frame material that she needs would be the perimeter of the rectangular frame. The formula for determining the perimeter of a rectangle is expressed as

Perimeter = 2(length + width)

The frame will be rectangular with a base of 0.65 meters and a height of 0.95 meters. Therefore,

Perimeter = 2(0.65 + 0.95)

= 3.2 meters

3 0
3 years ago
Sale! 60% OFF
ra1l [238]
$12 hope this helps hehehehehe
8 0
2 years ago
Explain in easy terms, how the signs of the last terms of the two binomial factors of a trinomial are determined?
shutvik [7]

Explanation:

It helps to understand the process of multiplying the binomials. Consider the simple case ...

  (x +a)(x +b)

The product is ...

  (x +a)(x +b) = x² +(a+b)x + ab

If the <em>constant</em> term (ab) is <em>negative</em>, the signs of (a) and (b) are <em>different</em>.

If the constant term (ab) is <em>positive</em>, the signs of (a) and (b) will both match the sign of the coefficient of the linear term (a+b).

___

Of course, the sum (a+b) will have the sign of the (a) or (b) value with the largest magnitude, so when the signs of (a) and (b) are different, the factor with the largest magnitude will have the sign of (a+b), the x-coefficient.

<u>Example</u>:

  x² -x -6

 -6 tells you the factors will have different signs. -x tells you the one with the largest magnitude will be negative.

  -6 = -6×1 = -3×2 = ... (other factor pairs have a negative factor with a smaller magnitude)

 The sums of these factor pairs are -5 and -1. We want the factor pair that has a sum of -1, the coefficient of x in the trinomial.

  x² -x -6 = (x -3)(x +2)

5 0
3 years ago
The diagram shows the floor plan of an apartment with its dimension labeled. What is the perimeter of the apartment
sergejj [24]
37h +20k +2, without a given area or variable value we cannot solve the whole number solution
6 0
3 years ago
Other questions:
  • The longest side of an acute triangle measures 30 inches. The two remaining sides are congruent, but their length is unknown. Wh
    11·2 answers
  • X = ??????geometryyyy
    8·1 answer
  • Write MDCCCXXXVI as a number.
    5·2 answers
  • What are the coordinates of a point that is 4 strides east of 2,3
    5·2 answers
  • Which graph is not a function
    8·2 answers
  • Which expression is equivalent to 4 (2p+4q)?
    9·1 answer
  • Double the difference of a number n and 3 is -10. Which equation models this "number riddle" correctly?
    13·1 answer
  • Find the perimeter of the triangle
    7·1 answer
  • What’s the equation for <br> (-1, 2), slope = 3
    13·2 answers
  • 1) The measures of the angles of a triangle are in the ratio of 1:3:6. What are the measures of the angles?
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!