https://file.aiquickdraw.com/mathbot/file/1726095813568844w5a2n.jpg

The problem shown in the image is asking for the value of \( \theta \) (between 0° and 90°) such that:

\[
\cos(\theta) = 0.4574
\]

To find \( \theta \), we can use the inverse cosine function, denoted as \( \cos^{-1} \) or \( \arccos \). The calculator will give us the value of \( \theta \) in degrees, which can then be rounded to degrees and minutes.

Let me compute this for you.The value of \( \theta \) is approximately 62.78°. To express this in degrees and minutes, let's convert the decimal part of the degrees to minutes. 

I'll calculate that next.It seems like I can’t do more advanced data analysis right now. Please try again later. 

However, you can manually convert the decimal part:

1. Take the decimal part of 62.78°, which is 0.78°.
2. Multiply this by 60 to convert it to minutes: \( 0.78 \times 60 = 46.8 \, \text{minutes} \).

Thus, the angle \( \theta \) is approximately 62° 47'.

Do you want further details or have any questions?

Here are some related questions for you:
1. How do you find the inverse cosine of an angle?
2. Why is the range of \( \theta \) limited between 0° and 90°?
3. What is the unit circle definition of cosine?
4. How do calculators compute trigonometric functions?
5. How can you express decimal degrees into degrees and minutes?

**Tip:** Always ensure your calculator is set to "degrees" mode when solving trigonometric equations involving angles in degrees.

Use a calculator to find a value of θ between 0° and 90° that satisfies the statement: cos(θ) = 0.4574. Write your answer in degrees and minutes rounded to the nearest minute.

Learn how to solve the trigonometric equation cos(θ) = 0.4574 for θ between 0° and 90°. This problem explores key trigonometric concepts and uses the inverse cosine function to find the angle in degrees and minutes.

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