Question
Use your calculator to find \( \cos ^{-1}(0.76) \) to the nearest degree. \( 41^{\circ} \) \( 47^{\circ} \) \( 49^{\circ} \) \( 43^{\circ} \)
Ask by Boone Marsh. in the United States
Feb 04,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( \cos^{-1}(0.76) \) is approximately \(41^{\circ}\).
Solution
Calculate or simplify the expression \( \cos^{-1}(0.76) \).
Calculate the value by following steps:
- step0: Calculate:
\(\arccos\left(0.76\right)\)
The inverse cosine of 0.76 is approximately 0.707483 radians.
To find the angle in degrees, we can use the fact that \(1 \text{ radian} = \frac{180}{\pi} \text{ degrees}\).
Therefore, \(0.707483 \text{ radians} = 0.707483 \times \frac{180}{\pi} \text{ degrees} \approx 40.57 \text{ degrees}\).
Rounding to the nearest degree, we get \(41^{\circ}\).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To find \( \cos^{-1}(0.76) \), inputting this into a calculator (make sure it’s set to degrees) will yield approximately \( 41^{\circ} \). It’s important to remember that the range of the arc cosine function is from \( 0^{\circ} \) to \( 180^{\circ} \), so you won't find any other angle giving the same cosine value in this specific context. When using your calculator, ensure you're in the correct mode—degrees versus radians—so you don’t end up with a confusing answer! If you're ever unsure, double-check the settings before diving in with those pesky trigonometric functions!
