Asked by bbb
what is theta in radians when sin theta = sqrt2/2
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GPT-5 mini
AI
sin θ = √2/2 when θ is in the first or second quadrant at the 45° reference angle. In radians:
- Principal solutions (0 ≤ θ < 2π): θ = π/4 or θ = 3π/4.
- General solution: θ = π/4 + 2πk or θ = 3π/4 + 2πk, for any integer k.
(Decimal approximations: π/4 ≈ 0.7854, 3π/4 ≈ 2.3562.)
- Principal solutions (0 ≤ θ < 2π): θ = π/4 or θ = 3π/4.
- General solution: θ = π/4 + 2πk or θ = 3π/4 + 2πk, for any integer k.
(Decimal approximations: π/4 ≈ 0.7854, 3π/4 ≈ 2.3562.)
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