Question

Solve sin theta + 1 = cos 2 theta on the interval 0 less than or equal to theta <2 pi

Answer 1

Answer:

Ф = 0 and Ф = π

Step-by-step explanation:

* Lets explain how to solve the problem

∵ sin Ф + 1 = cos²Ф, where 0 ≤ Ф < 2π

- To solve we must to replace cos²Ф by 1 - sin²Ф

∵ sin²Ф + cos²Ф = 1

- By subtracting sin²Ф from both sides

∴ cos²Ф = 1 - sin²Ф

- Lets replace cos²Ф in the equation above

∴ sin Ф + 1 = 1 - sin²Ф

- Subtract 1 from both sides

∴ sin Ф = - sin²Ф

- Add sin²Ф for both sides

∴ sin²Ф + sin Ф = 0

- Take sin Ф as a common factor from both sides

∴ sin Ф(sin Ф + 1) = 0

- Equate each factor by 0

∵ sin Ф = 0

∴ Ф = 0 OR Ф = 2π

∵ sin Ф + 1 = 0

- Subtract 1 from both sides

∴ sin Ф = -1

∴ Ф = π

∵ 0 ≤ Ф < 2π

∵ Ф < 2π

∴ We will refused the answer Ф = 2π

∴ Ф = 0 and Ф = π