Questions: Give the degree measure of θ if it exists. Do not use a calculator. θ=arccos (1) Select the correct choice below and fill in any answer boxes in your choice. A. θ=arccos (1)= 0 (Type your answer in degrees.) B. arccos (1) does not exist

Give the degree measure of θ if it exists. Do not use a calculator.

θ=arccos (1)

Select the correct choice below and fill in any answer boxes in your choice.
A. θ=arccos (1)= 0 (Type your answer in degrees.)
B. arccos (1) does not exist

Transcript text: Give the degree measure of $\theta$ if it exists. Do not use a calculator. \[ \theta=\arccos (1) \] Select the correct choice below and fill in any answer boxes in your choice. A. $\theta=\arccos (1)=$ $\square$ 0 (Type your answer in degrees.) B. $\arccos (1)$ does not exist

Solution

Solution Steps

To solve for $\theta$ in the equation $\theta = \arccos(1)$, we need to understand the definition of the arccosine function. The arccosine function, $\arccos(x)$, gives the angle whose cosine is $x$. Since $\cos(0) = 1$, $\arccos(1) = 0$ degrees.

Solution Approach

Recognize that $\arccos(1)$ is asking for the angle whose cosine is 1.
Recall that $\cos(0) = 1$, so $\arccos(1) = 0$ degrees.

Step 1: Understanding the Problem

We need to find the degree measure of $\theta$ where $\theta = \arccos(1)$. The arccosine function returns the angle whose cosine is equal to the given value.

Step 2: Evaluating $\arccos(1)$

The cosine of an angle is equal to 1 at $0$ degrees. Therefore, we have: \[ \arccos(1) = 0 \]

Step 3: Conclusion

Since we have determined that $\theta = 0$ degrees, we can express this in the final answer format.