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Chapter 4: Problem 63

Determine whether the statement is true or false. Justify your answer. The real number 0 corresponds to the point (0,1) on the unit circle.

Short Answer

Expert verified
The statement 'The real number 0 corresponds to the point (0,1) on the unit circle' is false. The correct point at 0 radians on the unit circle is (1,0).

Step by step solution

01

Understanding the problem

The problem asks to determine whether the statement 'The real number 0 corresponds to the point (0,1) on the unit circle' is true or false. Here, the real number mentioned is referring to an angle measure, usually in radians for the unit circle.
02

Recall the values of sin and cos at 0 radians

At 0 radians on the unit circle, \(\cos(\theta)\) = 1 and \(\sin(\theta)\) = 0. So, the point at 0 radians is (1,0).
03

Compare the given point with the actual point

The point corresponding to 0 on the unit circle is (1,0), but the given point is (0,1). Therefore, the statement is incorrect.

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