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^∘)

Want more problems? Check here!