To find the value of tan 315°, we can use the identity:
tan (θ + 180°) = tan θ
Since tan (315° + 180°) = tan 495°, and 495° is coterminal with 135°, we have:
tan 315° = tan (135° + 180°) = tan 135°
Using the fact that tan 45° = 1, and tan (θ + 90°) = -cot θ, we have:
tan 135° = tan (45° + 90°) = -cot 45° = -1
Therefore, the value of tan 315° is -1.