Find the Exact Value cos(-315 degrees )

Problem

cos(−315)

Solution

1. Use the even-odd property of the cosine function, which states that cos(−θ)=cos(θ)

cos(−315)=cos(315)

2. Find the coterminal angle or identify the position on the unit circle. The angle 315 is in the fourth quadrant.

315=360−45

3. Determine the reference angle by finding the distance to the nearest x-axis.

(θ_ref)=360−315=45

4. Determine the sign of the cosine function in the fourth quadrant. Since cosine represents the x-coordinate on the unit circle, it is positive in the fourth quadrant.

cos(315)=cos(45)

5. Evaluate the exact value using the known trigonometric values for special angles.

cos(45)=√(,2)/2

Final Answer

cos(−315)=√(,2)/2

Want more problems? Check here!