Find the Exact Value sin(145)

Problem

sin(145)

Solution

1. Identify the angle and the quadrant. The angle 145 is in the second quadrant because 90<145<180

2. Determine the reference angle. For an angle θ in the second quadrant, the reference angle θ′ is calculated as 180−θ

3. Calculate the reference angle value.

θ′=180−145=35

4. Apply the sign rule for the sine function. In the second quadrant, the sine of an angle is positive.

sin(145)=sin(35)

5. Evaluate the exactness. Since 35 is not a standard unit circle angle (like 30 45 or 60, its exact value is expressed simply as sin(35) or cos(55)

Final Answer

sin(145)=sin(35)

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