Problem 63
Question
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.
Step-by-Step Solution
Verified Answer
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).
1Step 1: 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.
2Step 2: 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).
3Step 3: 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.
Other exercises in this chapter
Problem 63
\(g\) is related to a parent function \(f(x)=\sin (x)\) or \(f(x)=\cos (x)\) (a) Describe the sequence of transformations from \(f\) to \(g\). (b) Sketch the gr
View solution Problem 63
Evaluate the sine, cosine, and tangent of the angle without using a calculator.
View solution Problem 63
Rewrite each angle in degree measure. (Do not use a calculator.) (a) \(\frac{5 \pi}{4}\) (b) \(-\frac{7 \pi}{3}\)
View solution Problem 63
A ball that is bobbing up and down on the end of a spring has a maximum displacement of 3 inches. Its motion (in ideal conditions) is modeled by \(y=\frac{1}{4}
View solution