find the value of 0 theta in the interval [0 degrees, 90 degrees] that satisfies the given statement cos 0 theta = 0.80596398

To find the value of \( \theta \) that satisfies the equation \( \cos \theta = 0.80596398 \), we will take the inverse cosine (arccos) of both sides of the equation. This will give us the angle \( \theta \) in degrees.

\[
\theta = \cos^{-1}(0.80596398)
\]

Let me calculate that for you.The value of \( \theta \) that satisfies \( \cos \theta = 0.80596398 \) in the interval \([0^\circ, 90^\circ]\) is approximately \( 36.30^\circ \).

Would you like further details on this or any other questions? Here are some related questions for practice:

1. What is the sine of \( \theta = 36.30^\circ \)?
2. How do you convert an angle from degrees to radians?
3. What is the value of \( \sin^{-1}(0.80596398) \)?
4. What is the unit circle definition of cosine?
5. How do you graph a cosine function?

**Tip**: Always ensure your calculator is set to the correct mode (degrees or radians) when working with trigonometric functions.

Find the value of theta in the interval [0 degrees, 90 degrees] that satisfies the given statement cos theta = 0.80596398

Learn how to find the angle theta in the interval [0°, 90°] where cos(θ) = 0.80596398. This trigonometry problem uses the inverse cosine (arccos) function to determine the correct angle, which is approximately 36.30°. Suitable for high school students in Grades 10-12.

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