For problems (a) through (d), give an answer between $0^{\circ}$ and $360^{\circ}$.
(a) What is the counterclockwise equivalent to a clockwise rotation of $690^{\circ}$ ?

Answer

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Answer

$\boxed{30^{\circ}}$ is the final answer

Steps

Step 1 ：Given a clockwise rotation of $690^{\circ}$

Step 2 ：A full rotation is $360^{\circ}$

Step 3 ：Since $690^{\circ}$ is more than one full rotation, we need to find the remainder of $690^{\circ}$ divided by $360^{\circ}$

Step 4 ：The remainder is $330^{\circ}$

Step 5 ：To find the counterclockwise equivalent, we subtract this remainder from $360^{\circ}$

Step 6 ：The counterclockwise equivalent is $30^{\circ}$

Step 7 ：$\boxed{30^{\circ}}$ is the final answer