Problem

Find the terminal point on the unit circle determined by 5π3 radians.
Use exact values, not decimal approximations.
(x,y)=(1,)

Answer

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Answer

Final Answer: The terminal point on the unit circle determined by 5π3 radians is (12,32)

Steps

Step 1 :The terminal point on the unit circle is given by the coordinates (cos(theta), sin(theta)). Here, theta is the angle in radians, which is given as 5π3. So, we need to find the cosine and sine of 5π3.

Step 2 :The cosine of 5π3 is approximately 0.5 and the sine of 5π3 is approximately -0.866. However, we need to provide the exact values.

Step 3 :The exact value of cos(5π3) is 12 and the exact value of sin(5π3) is 32.

Step 4 :Final Answer: The terminal point on the unit circle determined by 5π3 radians is (12,32)

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