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
denpristay [2]
3 years ago
13

Find all solutions of the equation in the interval [0, 2pi).

Mathematics
1 answer:
natali 33 [55]3 years ago
8 0

Answer:

Step-by-step explanation:

Begin by squaring both sides to get rid of the radical. Doing that gives you:

sin^2x=1-cosx

Now use the Pythagorean identity that says

sin^2x =1-cos^2x and make the replacement:

1-cos^2x=1-cosx. Now move everything over to one side of the equals sign and set it equal to 0 so you can factor:

1-cos^2x+cosx-1=0 and then simplify to

cosx-cos^2x=0

Factor out the common cos(x) to get

cosx(1-cosx)=0 and there you have your 2 trig equations:

cos(x) = 0 and 1 - cos(x) = 0

The first one is easy enough to solve. Look on the unit circle and see where, one time around, where the cos of an angle is equal to 0. That occurs at

x=\frac{\pi }{2},\frac{3\pi}{2}

The second equation simplifies to

cos(x) = 1

Again, look to the unit circle and find where the cos of an angle is equal to 1. That occurs at π only.

So, in the end, your 3 solutions are

x=\frac{\pi}{2},\pi,\frac{3\pi}{2}

You might be interested in
2x+y=10<br> Y=5x-11<br> Solve the system of equations by substitution
antoniya [11.8K]
The answer would be (3,4)
8 0
3 years ago
Read 2 more answers
Please help cause I don’t know how to do this
zalisa [80]

Answer:

  4 GB

Step-by-step explanation:

Let "g" represent the number of gigabytes of data used. Then the phone bill is computed as ...

  bill = 65 + 12g

Aurora's bill is 113, so we can put that value into the equation and solve for g.

  113 = 65 + 12g

  48 = 12g . . . . . . subtract 65 from both sides of the equation

  4 = g . . . . . . . . . divide both sides of the equation by 12

Aurora used 4 gigabytes of data in September.

_____

You can also use your mathematical reasoning to solve this problem. The total bill consists of two charges: a fixed charge of 65 and a charge that depends on data. If you subtract the fixed charge from the bill, you find that the charge that depends on data is 113-65 = 48.

The data charge is 12 times the number of gigabytes. The data charge on the bill is 48, which is 12 times 4. Then the number of gigabytes is 4.

7 0
3 years ago
What is the splitting of an atom called?
Marysya12 [62]

Answer:

fission

hope this helps (:

7 0
3 years ago
Read 2 more answers
What is the simplest form of the fraction 120/150?
kolbaska11 [484]

Answer:

4/5

Step-by-step explanation:

120/30=4

150/30=5

120/150=4/5

6 0
3 years ago
Read 2 more answers
What is the are and perimeter of these 4 problems
Allisa [31]

Answer:

1.A:32 P:24

2.A:40 P:26

Step-by-step e1.xplanation:

2. its the same as a rectangle if you cut it you can turn it into a rectangle

7 0
3 years ago
Other questions:
  • -10n + 24 + 30n = -36<br> Solve this equation
    9·2 answers
  • A package of 5 pairs of insulated socks costs $36.95. What is the unit price of the pairs of socks
    12·2 answers
  • When multiplying two numbers written in scientific notation, what do you do with the exponents of the 10?
    14·1 answer
  • Price-club sells a 12-ounce box of crackers for $2.59 and Shop Mart sells 1-1/2 pound box of crackers for $4.68. What is the uni
    7·2 answers
  • need help asap plzz.Solve the inequality. (x + 19 ≤ −5). (A)x ≤ −14 (B)x ≤ 24 (C)x ≤ −24 (D)x ≤ 14
    8·1 answer
  • Factorize: (a+b)^2 + 4 (a+b)+ 4
    8·1 answer
  • NEED HELP ASAP PLEASE :(
    12·1 answer
  • Please please help please please help me please please help
    11·1 answer
  • HELP PLEASE ITS DUE TODAY!!! Express 14 hours in 2 weeks as a unit rate
    8·1 answer
  • What would these be reflected as?
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!