Answer:
Θ = 0, π, 
, 
Step-by-step explanation:
Using the identity
cos2Θ = 1 - 2sin²Θ, then
sinΘ + 1 = 1 - 2sin²Θ ( subtract 1 - 2sin²Θ from both sides )
2sin²Θ + sinΘ = 0 ← factor out sinΘ from each term
sinΘ(2sinΘ + 1) = 0
Equate each factor to zero and solve for Θ
sinΘ = 0, hence
Θ = 
(0) = 0, π, 2π
2sinΘ + 1 = 0 → sinΘ = - 
, thus
Θ = ( - ) = - 
Since sinΘ < 0 then Θ is in third/ fourth quadrants, thus
Θ = π + = or Θ = 2π - =
Solution is
Θ = 0, π, , for 0 ≤ Θ < 2π
Answer:
7
Step-by-step explanation:
Answer:
The answer to your question is:
Step-by-step explanation:
Q1. They are vertical angles, so they measure the same
[2(x + 10)] = (3x - 30)
2x + 20 = 3x -30
2x - 3x = -30 - 20
- x = - 50
x = 50
Q2. They are also vertical angles, so they measure the same.
[6(x - 2)] = 3x + 30
6x - 12 = 3x + 30
6x - 3x = 30 + 12
3x = 42
x = 42/3
x = 14
∠DHG = 6(14 - 2)
∠DHG = 6(12)
∠DHG = 72
Answer:
x<3
Step-by-step explanation:
23-6x>5
6x>23-5
6x>18
x>18/6
x>3
x<3
