Find the Exact Value sin(-240 degrees )

Problem

sin(−240^∘)

Solution

1. Find the coterminal angle by adding 360^∘ to the negative angle to find its equivalent position within the standard 0^∘ to 360^∘ range.

sin(−240^∘)=sin(−240^∘+360^∘)

sin(−240^∘)=sin(120^∘)

2. Identify the quadrant for 120^∘ Since 90^∘<120^∘<180^∘ the angle lies in Quadrant II, where the sine function is positive.

3. Determine the reference angle by subtracting the angle from 180^∘

(θ_ref)=180^∘−120^∘

(θ_ref)=60^∘

4. Apply the reference angle and the sign from the quadrant to find the exact value.

sin(120^∘)=sin(60^∘)

sin(60^∘)=√(,3)/2

Final Answer

sin(−240^∘)=√(,3)/2

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