Find the Exact Value sin(310)

Problem

sin(310^∘)

Solution

1. Identify the angle and its quadrant. The angle 310^∘ is in the fourth quadrant because 270^∘<310^∘<360^∘

2. Determine the sign of the sine function in the fourth quadrant. In the fourth quadrant, the sine value is negative.

3. Calculate the reference angle. The reference angle (θ_R) for an angle in the fourth quadrant is found using 360^∘−θ

(θ_R)=360^∘−310^∘

(θ_R)=50^∘

4. Express the value in terms of the reference angle.

sin(310^∘)=−sin(50^∘)

5. Evaluate if the angle is a standard trigonometric angle. Since 50^∘ is not a standard angle (like 30^∘ 45^∘ or 60^∘, the exact value is written in terms of the sine function.

Final Answer

sin(310^∘)=−sin(50^∘)

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