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The question on the image asks to find a value of \( \theta \) in the interval \( [0^\circ, 90^\circ] \) that satisfies the equation:

\[
\cos \theta = 0.82063405
\]

We can solve for \( \theta \) by using the inverse cosine (arccos or \( \cos^{-1} \)) function. Let's calculate the value of \( \theta \).

I will compute this value for you.The value of \( \theta \) that satisfies \( \cos \theta = 0.82063405 \) in the interval \( [0^\circ, 90^\circ] \) is approximately:

\[
\theta \approx 34.851685^\circ
\]

Would you like more details on how this was calculated, or have any questions?

Here are 5 related questions for further practice:
1. What is the sine of \( \theta = 34.851685^\circ \)?
2. How do you find \( \theta \) when given a sine value instead?
3. What is the value of \( \cos \theta \) when \( \theta = 45^\circ \)?
4. How can you calculate \( \theta \) if given a tangent value?
5. What happens to the cosine function as \( \theta \) approaches \( 90^\circ \)?

**Tip:** Always check that your calculator is set to degrees or radians based on the problem you're solving!

Find a value of θ in the interval [0°, 90°] that satisfies the given statement. cos θ = 0.82063405

Solve for θ in the interval [0°, 90°] where cos θ = 0.82063405. Learn how to use the inverse cosine function (cos⁻¹) to calculate the angle, and get step-by-step solutions. This problem is suitable for high school students studying trigonometry.

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