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
tangare [24]
3 years ago
8

Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal plac

es where appropriate. If there is no solution, enter NO SOLUTION.) 8 sin(2θ) − 2 sin(θ) = 0
Mathematics
1 answer:
Fed [463]3 years ago
8 0

Answer:

\theta=k\pi, \hspace{3}k\in Z\\\\ or\\\theta =2\pi k \pm arccos(\frac{1 }{8} ), \hspace{3}k\in Z\\

Step-by-step explanation:

Factor constant terms:

-2(-4sin(2\theta)+sin(\theta))=0

Divide both sides by -2:

sin(\theta)-4sin(2 \theta)=0

Expand trigonometric functions using the fact:

sin(2 \theta) =2 sin(\theta) cos(\theta)

So:

sin(\theta) -8sin(\theta)cos(\theta)=0

Factor sin(x) and constant terms and multiply both sides by -1:

sin(\theta) (8cos(\theta)-1)=0

Split into two equations:

(1)=8cos(\theta)-1=0\\\\(2)=sin(\theta)=0

For (1)

Add 1 to both sides and divide both sides by 8:

cos(\theta)=\frac{1}{8}

Take the inverse cosine of both sides:

\theta =2\pi k \pm arccos(\frac{1 }{8} ), \hspace{3}k\in Z

For (2)

Simply take the inverse sine of both sides

\theta = k \pi, \hspace{3}k\in Z

Therefore, the solutions are given by:

\theta=k\pi, \hspace{3}k\in Z\\\\ or\\ \theta =2\pi k \pm arccos(\frac{1 }{8} ), \hspace{3}k\in Z\\

You might be interested in
A Circus charges two dollars and 50 Cent for kids tickets and six dollars for adults tickets. Last weekend, twice as many kids a
Sloan [31]

Answer: The answer is 2,860.

Step-by-step explanation:

6 0
3 years ago
The area of a cylinder's base is 706.5 square millimeters. The cylinder's lateral area is 471 square millimeters. What is the to
Rzqust [24]
Just add the two bases plus the lateral area. so it would be 706.5+706.5+471.
8 0
3 years ago
Read 2 more answers
Which statements are true regarding the area of circles & sectors? Check all that apply.
Fynjy0 [20]

Answer:

4pi r

Step-by-step explanation:

7 0
3 years ago
What is an equation of the line that passes through the point (-6, -7) and is
Alexandra [31]

Answer:

Step-by-step explanation:

Product of slope of perpendicular lines = -1

6x + 5y = 30

Write this equation in y = mx + b  form

        5y = -6x + 30

          y = \frac{-6}{5}x+\frac{30}{5}

          y=\frac{-6}{5}x + 6

Slope of this line m₁ = -6/5

m₁ * m₂ = -1

      m₂ = -1÷m₁ = -1 * \frac{5}{-6}  

m_{2}=\frac{5}{6}     & (-6 , -7)

Equation of the required line: y - y₁ = m (x - x₁)

y - (-7) = \frac{5}{6}(x - [-6])\\\\y + 7 = \frac{5}{6}x + 6 *\frac{5}{6}\\\\y = \frac{5}{6}x +5-7\\\\y=\frac{5}{6}x-2

8 0
3 years ago
How might a change in the environment affect plants differently than it would animals?
valentina_108 [34]

Answer:

Some plants need certain things in their environment, so if their environment changes it could make the plants not grow. Animals would most likely either move to a different area or would get used to the change.

8 0
3 years ago
Other questions:
  • What is the sum of 171
    8·1 answer
  • How do I solve 2 3/4 -6 7/20, -2 3/5 - 6 /2/3, and 4 2/3 / 6 3/4?
    8·1 answer
  • Martha's house is 17 m long and 21 m wide. How long is the diagonal of the house?
    7·1 answer
  • The coordinate grid shows the graph of four equations Which set of equations has (3, 1) as its solution?
    10·1 answer
  • A video game system and several games are sold for $ 648. The cost of the games is 3 times as much as the cost of the system. Fi
    10·1 answer
  • A pharmacist receives a shipment of 1717 bottles of a drug and has 44 of the bottles tested. If 44 of the 1717 bottles are conta
    6·1 answer
  • Express as a trinomial. (2x+5)(3x-4)
    14·1 answer
  • Find the equation of the line through the points (6, -9) and (-2, -1).
    13·1 answer
  • Two students were shopping for school supplies. They need spirals which cost x dollars and pens which cost y dollars. One studen
    5·1 answer
  • Determine the angle of elevation if the slope is 0.3415
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!