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
olganol [36]
3 years ago
10

Solve sin θ +1 = cos2 θ on the interval 0 less than or equal to θ less than 2pi

Mathematics
1 answer:
valkas [14]3 years ago
8 0

Answer:

The solution of the equation is Ф = 0 or Ф = 3π/2

Step-by-step explanation:

* Lets revise some facts in trigonometry

- The identity sin² Ф + cos² Ф = 1

- By subtracting sin² Ф from both sides then cos² Ф = sin² Ф - 1

- In the rectangular plane the point (x , y) represents  (cos Ф , sin Ф)

 where x = cox Ф and y = sin Ф

- The point (1 , 0) lies on the positive part of x-axis means cos Ф = 1

 and sin Ф = 0, then Ф = 0 or 2π

- The point (-1 , 0) lies on the negative part of x-axis means cos Ф = -1

 and sin Ф = 0, then Ф = π

- The point (0 , 1) lies on the positive part of y-axis means cos Ф = 0

 and sin Ф = 1, then Ф = π/2

- The point (0 , -1) lies on the negative part of y-axis means cos Ф = 0

 and sin Ф = -1, then Ф = 3π/2

* Lets solve the problem

∵ sin Ф + 1 = cos² Ф

- To solve we must change cos² Ф to sin² Ф

∵ cos² Ф = sin² Ф - 1

- substitute cos² Ф in the equation by 1 - sin² Ф

∴ sin Ф + 1 = 1 - sin² Ф ⇒ add sin² Ф to both sides

∴ sin² Ф + sin Ф + 1 = 1 ⇒ subtract 1 from both sides

∴ sin² Ф + sin Ф = 0

- Take sin Ф as a common factor from both terms

∴ sin Ф (sin Ф + 1) = 0

- Equate each factor by 0

∴ sin Ф = 0 OR sin Ф + 1 = 0

- Remember 0 ≤ Ф < π

∵ sin Ф = 0 ⇒ from the information above

∴ Ф = 0

∵ sin Ф + 1 = 0 ⇒ subtract 1 from both sides

∴ sin Ф = -1

- From the information above

∴ Ф = 3π/2

* The solution of the equation is Ф = 0 or Ф = 3π/2

You might be interested in
Mr. Huyck needs 8 gallons of punch for the school dance. How many<br> quarts of punch would he need?
koban [17]
32 bc eight times four equals 32
8 0
3 years ago
Read 2 more answers
Find the diameter of the object.
Anni [7]

Answer:

1 \frac{1}{5} centimeters

Step-by-step explanation:

The diameter is equal to the radius × 2. We know that the radius is equal to 3/5 centimeters.

To solve this you must do \frac{3}{5} × 2.

This equals \frac{6}{5}, or 1 \frac{1}{5} cm.

5 0
3 years ago
Simple math! ( i'll mark you)
LenKa [72]

Answer:

234

Step-by-step explanation:

Glad to help mark me

5 0
2 years ago
Read 2 more answers
Help this is due today
Gelneren [198K]

Answer:

2 1/2 I think

Step-by-step explanation:

you find the L.C.M for all the fractions and multiply it. You should end up with whole numbers.

It should look like this

2n+3n=2

n= <u>2n+3n</u><u> </u> = <u>5</u>

2 2

n= 2 1/2

8 0
2 years ago
What is the circumference
Butoxors [25]
Are you asking for the definition of circumference? because you didn’t attach a picture or give us an equation to do.
5 0
3 years ago
Other questions:
  • Elisa sold 110 tickets for the football game. Adult tickets cost $2.50 and student tickets cost $1.10. If she collected $212, ho
    8·1 answer
  • Answer 1-9 please help i will give thanks or brainiest 10 points
    7·1 answer
  • 8 x 2/3 x (-6) x (3/4) x (-1)
    12·1 answer
  • Write the numerical
    9·1 answer
  • Ruth Brown wants to borrow $2,600 for 90 days to pay her real 'estate tax. State Savings and Loan charges 7.25% ordinary interes
    12·1 answer
  • Simplify (9+7i)/(-10+8i)
    5·1 answer
  • Aspirin is sold in boxes of 24 for $3.69, 50 for $5.49, 100 for $8.29, and 150 for $11.99. Which box has the best unit rate.
    14·1 answer
  • What’s the range?????? :(
    10·1 answer
  • What is the solution to the system of equations? 2x – y = 7 y = 2x 3
    10·1 answer
  • Right triangle has a shorter leg of 5, a longer leg of 7. What is the length of the hypotenuse? Round to the nearest hundredth.
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!