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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