Show that the point (-2 Squareroot 2/3, -1/3) is on the unit circle. The point P

Question

Show that the point (-2 Squareroot 2/3, -1/3) is on the unit circle. The point P(x, y) is on the unit circle in quadrant II. If x = -Squareroot 11/6, find y. Find the reference number and the terminal point P(x, y) determined by t = 19 pi/6. Suppose that the terminal point determined by t is the point (5/13 middot 12/13) on the unit circle. Find the terminal point determined by 2 pi - t. Find the reference number for t = -22/3 pi. Find the exact value of sin(19 pi/6) and cos(-5 pi/6). Find the exact value of tan(7 pi/2) and cot (-7 pi/2). If the terminal point determined by t is (12/13, -5/13), find sin t, cos t and tan t.

Explanation / Answer

If the point is on the unit circle then the radius=1 unit that is the distance from the origin to the point is 1

d=(sqrt(0+2sqrt2/3)2+(0+1/3)2) = sqrt(8/9 +1/9)=sqrt(9/9)=1

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