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

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

it’s supposed to be -4+45=41

step-by-step explanation:

25 questions , because they start with 100.  

350-100=250 .  

. 250/10=25

step-by-step explanation:

first take off 100, then what x 10 = 250? that is your answer. (25)