The equation \( \sec(\theta) = 2.445 \) can be solved for \( \theta \) by finding the inverse of the secant function. Recall that:

\[
\sec(\theta) = \frac{1}{\cos(\theta)}
\]

So, if \( \sec(\theta) = 2.445 \), we have:

\[
\cos(\theta) = \frac{1}{2.445}
\]

Now, let's calculate this:

\[
\cos(\theta) = 0.4089
\]

To find \( \theta \), take the inverse cosine (\( \cos^{-1} \)) of 0.4089:

\[
\theta = \cos^{-1}(0.4089)
\]

Using a calculator, we get:

\[
\theta \approx 66.0^\circ \text{ or } 1.152 \, \text{radians}
\]

Since secant is periodic, there are multiple possible solutions. The general solution for \( \theta \) can be written as:

\[
\theta = 66^\circ + 360^\circ n \quad \text{or} \quad \theta = 294^\circ + 360^\circ n
\]

where \( n \) is any integer.

Would you like further details or a breakdown of the steps?

Here are 5 related questions:
1. How do you find the secant of an angle?
2. What is the relationship between secant and cosine?
3. How does the periodicity of the secant function affect solutions?
4. What is the general solution for trigonometric equations?
5. How do you convert between degrees and radians?

**Tip:** Always remember to consider all possible solutions when solving trigonometric equations due to their periodic nature.

Learn how to solve the trigonometric equation sec(θ) = 2.445 by finding the inverse of the secant function. This solution involves key concepts in trigonometry such as secant, cosine, and inverse functions. Suitable for students in Grades 10-12.

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