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calculus

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A. a particle moves around the circle x^2+y^2 = 1 in such a way that the x coord rate of change is dx/dt= y
B) IS THE PARTICLE MOVING CLOCKWISE OR COUNTERCLOCKWISE AROUND THE CIRCLE

C) FROM THE RT TRIANGLE ONE CAN SEE THAT SIN(THETA) = Y AND COS(THETA) = X
USE THESE RELATIONS TO SHOW THAT THE ANGLE THETA IS CHANGING AT A CONST. RATE AND THEN FIND THAT RATE

  • calculus -

    B)CLOCKWISE
    In 1st quadrant (for ex.)dx/dt>0, so
    x increases;

    C)dx/dt=d(cos(theta))/dt=
    d(cos(theta))/d(theta)*d(theta)/dt=
    -sin(theta)*d(theta)/dx, so

    dx/dt=-y*d(theta)/dt =>d(theta)/dt=-1

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