Question

Trigonometry
Trigonometric Equations
0 ≤ x ≤ 2 π , solve the equation, sin 2θ =-1

Answer 1

θ = 3π/4, 7π/4

Explanation:

sin 2θ = -1

basic angle = π/2

2θ = 2π - π/2 = 3π/2,

3π/2 + 2π = 7π/2

θ = 3π/4, 7π/4

Answer 2

Explanation:

`sin ~2~ \theta=-1=-sin~ \pi /2\\=sin ~(\pi +\pi /2),sin ~(2\pi +\pi +\pi /2)\\=sin~(3\pi /2),sin~(7\pi /2)\\2 ~\theta=3 \pi/2,7 \pi /2\\\theta=3\pi /4,7\pi /4`