Solve \(\sin(θ)~=~\sqrt{3}/2\) for \(θ\) in \([0,~2\pi~)\). Use the diagram to state the reference angle, valid unit-circle locations, and complete solution set.

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The reference angle is pi/3; the valid locations are Quadrants I and II; the solution set is pi/3, 2pi/3.

The reference angle is pi/3; the only selected location is Quadrant I; the solution set is pi/3.

The reference angle is pi/3; the selected locations are Quadrants III and IV; the solution set is 4pi/3, 5pi/3.

The reference angle is pi/3; the selected locations are Quadrants I and II plus the excluded endpoint; the solution set is pi/3, 2pi/3, 2pi.

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Curriculum context

Course: Math III
Standard: F-TF.2
Category: Functions
Domain: Trigonometric Functions
Objective: Use the unit circle to extend trig functions to all real-number radian measures.
Problem type: Find the complete exact sine solution set on one period