Problem 33 Find the inclination $\theta$ ... [FREE SOLUTION]

Chapter 6: Problem 33

Find the inclination $\theta$ (in radians and degrees) of the line passing through the points. $$\left(\frac{1}{4}, \frac{3}{2}\right),\left(\frac{1}{3}, \frac{1}{2}\right)$$

Short Answer

Expert verified

The inclination of the line passing through the points $\left(\frac{1}{4}, \frac{3}{2}\right)$ and $\left(\frac{1}{3}, \frac{1}{2}\right)$ is $ \theta $ (in radians) and $ \theta $ degrees (after rounding to the nearest tenth).

Step by step solution

Calculate the slope

The formula to calculate the slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $ m = \frac{y_2 - y_1}{x_2 - x_1} $. Substituting the given points $\left(\frac{1}{4}, \frac{3}{2}\right)$ and $\left(\frac{1}{3}, \frac{1}{2}\right)$ into the formula, we get $ m = \frac{\frac{1}{2} - \frac{3}{2}}{\frac{1}{3} - \frac{1}{4}} $

Calculate the angle of inclination in radians

The slope is the tangent of the angle $\theta$ of inclination. So, we can use the inverse tangent function to get the angle: $ \theta = \text{arctan}(m) $. Substituting the calculated slope from the previous step, we find $ \theta $ in radians.

Convert radians to degrees

The conversion between radians and degrees is given by the equation $ \text{Degrees} = \text{Radians} \times \frac{180}{\pi} $. Applying this to the calculated $ \theta $ value, we get the angle in degrees.

Round the angles

If the results from steps 2 and 3 are not exact numbers, round to the nearest tenth for cleanliness and understanding.

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91影视

Find the inclination \(\theta\) (in radians and degrees) of the line passing through the points. $$\left(\frac{1}{4}, \frac{3}{2}\right),\left(\frac{1}{3}, \frac{1}{2}\right)$$

Short Answer

Step by step solution

Calculate the slope

Calculate the angle of inclination in radians

Convert radians to degrees

Round the angles

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