Solve for θ in: sin(2θ − 10°) = −0.5 where 0° ≤ θ ≤ 360°

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ScanSolve AI Tutor · Accepted Answer

Step 1: Start with the given equation. 0.5 tan² B − 0.5 = 0 Step 2: Add 0.5 to both sides. 0.5 tan² B = 0.5 Step 3: Divide both sides by 0.5. tan² B = 1 Step 4: Take the square root of both sides. tan B = ± 1; Step 5: Solve tan B = 1 for B ∈ [0°, 360°). The reference angle is 45°. General solution: B = 45° + 180° k, k ∈ Z. B = 45°, 45° + 180° = 225°; Step 6: Solve tan B = −1 for B ∈ [0°, 360°). The reference angle is 45°. Solutions in quadrants II and IV: B = 180° − 45° = 135°, 360° − 45° = 315° Step 7: All solutions: B = 45°, 135°, 225°, 315° 45°, 135°, 225°, 315°

Solve for θ in: sin(2θ - 10°) = -0.5 where 0° ≤ θ ≤ 360°

Answer

Step-by-step solution

Start with the given equation.

Add 0.5 to both sides.

Divide both sides by 0.5.

Take the square root of both sides.

Solve $\tan B = 1$ for $B \in [0^\circ, 360^\circ)$ .

Solve $\tan B = -1$ for $B \in [0^\circ, 360^\circ)$ .

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