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

Answer:The solution of the equation is Ф = 0 or Ф = 3π/2Step-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