In the polar coordinate system, O is the pole, set a (4, π 6), B (2, 5 π 6), then the area of triangle OAB is______ ．

In the polar coordinate system, O is the pole, set a (4, π 6), B (2, 5 π 6), then the area of triangle OAB is______ ．

From the polar coordinates of a and B, we can get OA = 4, OB = 2, ∠ AOB = 5 π 6 − π 6 = 2 π 3. From the sine theorem of triangle area, we can get S & nbsp; △ OAB = 12oa × ob × sin2 π 3 = 23, so the area of OAB is 23, so the answer is 23

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