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
María bought five apples for 20 cents each, she also bought three pounds of bananas for 25 cents per pound. How much did she spe
gulaghasi [49]

Answer:

She spend $2.00.

Step-by-step explanation:

8 0
3 years ago
What is 125^2/3 in simplest form? and What is \sqrt[5]({-245} ) ^{5} in simplest form?
Natasha_Volkova [10]
{ 125 }^{ \frac { 2 }{ 3 }  }\\ \\ ={ \left( { 125 }^{ \frac { 1 }{ 3 }  } \right)  }^{ 2 }\\ \\ ={ \left( \sqrt [ 3 ]{ 125 }  \right)  }^{ 2 }\\ \\ ={ 5 }^{ 2 }\\ \\ =25

This is because:

{ a }^{ \frac { m }{ n }  }\\ \\ =\sqrt [ n ]{ { a }^{ m } }

Remember that:

5 x 5 x 5 = 125
5 0
3 years ago
Is how many sixth graders attend your school a statistical question?
HACTEHA [7]
Yes, any question that involves numbers would be a statistical question. 
8 0
3 years ago
Read 2 more answers
-4x = 16<br><br> a -64<br><br><br><br><br> b 4<br><br><br><br><br> c 20<br><br><br><br><br> d-4
cricket20 [7]

-4× = 16 answer: -4

Step-by-step explanation:

-4 × -4 = 16

4 0
2 years ago
I need help with this..... please help thank you
Papessa [141]

Answer:

option C is the correct answer because the continents used to be part of a larger supercontinent called Pangea and when the continents split the fossils went with it

4 0
2 years ago
Read 2 more answers
Other questions:
  • Suppose you are investigating which hamburger condiment is most popular in a school cafeteria. which measure of central tendency
    7·2 answers
  • Need ANSWER ASAPpppp
    12·2 answers
  • The Nellie Mae organization conducts an extensive annual study of credit card usage by college students. For their 2004 study, t
    11·1 answer
  • Andrea had 32 problems to do for mathematics homework over the weekend. She did 1/4 of the problems on Friday night, and on Satu
    12·1 answer
  • What are the exact lengths of BC and CF?
    12·2 answers
  • PLS HELP Hannah and Brooklyn are two of the partners in a business. Hannah makes $3 in profit for every $4 that Brooklyn makes.
    14·1 answer
  • -5/2a+5=25 what does a equal
    8·1 answer
  • Three of these turtles weight 1,050 pounds. How much does one Pinta Island Tortoise weight?
    13·2 answers
  • The cost of a Kit-Kat is $0.04 more than the cost of a Snickers. If you buy 4 Kit-Kats and 8 Snickers, the total cost is $12.76.
    10·1 answer
  • The price for renting a movie in 5 stores is shown below. Which TWO data measures are represented by $5? plz help
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!