The following questions concern the algebraic relations among angular and linear

Question

The following questions concern the algebraic relations among angular and linear coordinates. Assume that the point in question has x(t) = r cos[(t)] and that y(t) = rsin[(t)]. (a) What is the algebraic expression for the speed v for uniform circular motion in terms of the point's angular speed  and radius r? (Use "omega" for  and "r" for r as necessary.)
v = r*

(b) For uniform circular motion, what is the algebraic expression for (t) in terms of the initial angle 0, the angular speed  and t? (Use "theta_0" for 0, "omega" for  and "t" for t, as necessary.)
(t) =  0 + *t

(c) What is the algebraic expression for the x-position implied by the formula given in part (b)? You want x(t) in terms of r, 0,  and t. (Use same typed variable names as above, along with "r" for r.)
x(t) = ________ 

(d) What is the algebraic expression for the x-velocity vx(t) implied by the formula given in parts (b) and (c)? You want vx(t) in terms of r, 0,  and t. (Use same typed variable names as above.)
vx(t) =_________

The answers of A and B are correct. But I don't know how to type the equations for part c and d. 

Thank you.

Explanation / Answer

(c)just substitute the value of in x(t)

x(t)= rcos(0 +*t)

(d)differentiate x(t) given in (c) with respect to t

   v(t)= -rsin(0+t)

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