Point P is located at (4.3 cm, 3.6 cm) in a two-dimensional Cartesian coordinate system. Calculate the angle in degrees between the x-axis and the line connecting the origin to point P.

Mathematics · College · Thu Feb 04 2021

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To calculate the angle between the x-axis and the line connecting the origin (0, 0) to the point P (4.3 cm, 3.6 cm), we can use trigonometry. The angle we are interested in, let's call it θ (theta), can be found by calculating the arctangent of the ratio of the y-coordinate to the x-coordinate of point P.

Here are the logical steps to follow:

1. Identify the coordinates of point P, which are (x, y) = (4.3 cm, 3.6 cm). 2. Use the formula for the arctangent (tan⁻¹) to find the angle θ. The formula is: θ = tan⁻¹(y/x) 3. Plug in the values for point P into the formula: θ = tan⁻¹(3.6/4.3) 4. Use a calculator to find the arctangent of the division (make sure the calculator is set to degrees): θ ≈ tan⁻¹(0.8372...) 5. Calculate the value to get the angle in degrees: θ ≈ 39.8 degrees

Therefore, the angle in degrees between the x-axis and the line connecting the origin to point P is approximately 39.8 degrees.

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