Question

Solve the following for θ, in radians, where 0≤θ<2π.

−sin2(θ)−2sin(θ)+1=0
Select all that apply:

0.75
2.5
2.71
0.95
0.43
2.04

Answer 1

Answer:2.71

0.43 are correct

Step-by-step explanation:We can solve this quadratic equation in sin(θ) by using the substitution u = sin(θ):

-u^2 - 2u + 1 = 0

Multiplying both sides by -1, we get:

u^2 + 2u - 1 = 0

We can use the quadratic formula to solve for u:

u = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = 2, and c = -1. Substituting these values, we get:

u = (-2 ± sqrt(4 + 4)) / 2

u = (-2 ± 2sqrt(2)) / 2

Therefore, either: