Find the Exact Value sin(-330 degrees )

Problem

sin(−330^∘)

Solution

1. Find the coterminal angle by adding 360^∘ to the given negative angle to find an equivalent angle between 0^∘ and 360^∘

−330^∘+360^∘=30^∘

2. Apply the property of trigonometric functions where sin(θ+360^∘⋅n)=sin(θ)

sin(−330^∘)=sin(30^∘)

3. Determine the exact value using the unit circle or special right triangles for a 30^∘ angle.

sin(30^∘)=1/2

Final Answer

sin(−330^∘)=1/2

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