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
Margaret [11]
3 years ago
15

Sin (x/2)= √2- sin (x/2) solve for the exact solutions in the interval (0, 2π)

Mathematics
1 answer:
serg [7]3 years ago
5 0

sin\left( \frac{x}{2} \right)=\sqrt{2}-sin\left( \frac{x}{2} \right)\implies sin\left( \frac{x}{2} \right)+sin\left( \frac{x}{2} \right)=\sqrt{2}\implies 2sin\left( \frac{x}{2} \right)=\sqrt{2} \\\\\\ sin\left( \cfrac{x}{2} \right)=\cfrac{\sqrt{2}}{2}\implies sin^{-1}\left[ sin\left( \cfrac{x}{2} \right) \right]=sin^{-1}\left( \cfrac{\sqrt{2}}{2} \right) \implies \cfrac{x}{2}= \begin{cases} \frac{\pi }{4}\\\\ \frac{3\pi }{4} \end{cases} \\\\[-0.35em] ~\dotfill

\cfrac{x}{2}=\cfrac{\pi }{4}\implies \boxed{x=\cfrac{\pi }{2}}~\hfill \cfrac{x}{2}=\cfrac{3\pi }{4}\implies \boxed{x=\cfrac{3\pi }{2}}

You might be interested in
The number of bacteria grew from 275 to 1135 in 3 hours. Find the number of bacteria to grow to 5000
ch4aika [34]

Answer:

4 hours

Step-by-step explanation:

5000 divided by 1135

8 0
3 years ago
Read 2 more answers
Plz help me get the answer
Igoryamba

1/2 a ≤ 12

2(1/2 a) ≤ 2(12)

2/2 a ≤ 24

1a ≤ 24

a ≤ 24

5 0
3 years ago
Read 2 more answers
Y=1/6x + 5 what is the answer
kykrilka [37]
X should equal  6y-30
3 0
3 years ago
Working alone, it takes Julia 16 hours to clean an attic. Lea can clean the same attic in 15 hours. If they worked together how
egoroff_w [7]
How do you think we set this problem up?

7 0
3 years ago
Chandler wants to raise 200$ to buy a new gaming system. He already has 80$ and plans to save 40$ a week. How many weeks will it
SashulF [63]

Answer:

<h2>3 weeks</h2>

Step-by-step explanation:

Step one:

given data

expected amount =$200

cash already at hand=$80

savings per week=$40

let the number of weeks be x

Step two:

the linear function for the situation is the same as the equation of a straight line

y=mx+c------1

200=4x+80

solve for x

200-80=40x

120=40x

divide both sides  by 4

x=120/40

x= 3 weeks

<u>Chandler will save for 3 weeks</u>

4 0
3 years ago
Other questions:
  • Find two consecutive whole numbers that the square root of 47<br> lies between.
    15·1 answer
  • In an online practice test, Sam got 11 correct answers. However, 3.5 points were deducted for incorrect answers. If he scored 18
    11·1 answer
  • Determine the solution set of x^2-80=0
    9·1 answer
  • Ben works in a sandwich shop. On average, he makes 3 sandwiches every 10 minutes. If Ben works 6 hours how many sandwiches will
    13·1 answer
  • What is the square root of 27/64 to the 3rd power
    15·1 answer
  • An object is launched directly upward with an initial velocity of 64 feet per second from a platform 80 feet high. What will be
    15·1 answer
  • Larry paid $3.20 for 64 ounces of milk. How much did each ounce cost?
    7·1 answer
  • 1 1 point
    14·1 answer
  • Are you gay..........................
    12·2 answers
  • Simplify.
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!