Problem

The point $\mathrm{P}(-7,-2)$ lies on the terminal arm of an angle $\theta$ in standard position. Determine the measure of $\theta$. Round your answer to 4 decimal places. Use $\pi$ $=3.14159$ if needed.

Solution

Step 1 :Given point P(-7, -2) lies on the terminal arm of an angle \(\theta\) in standard position.

Step 2 :Find the tangent of the angle \(\theta\): \(\tan(\theta) = \frac{y}{x} = \frac{-2}{-7}\)

Step 3 :Use the arctangent function to find the angle \(\theta\): \(\theta = \arctan(\frac{-2}{-7})\)

Step 4 :Since point P is in the third quadrant, add \(\pi\) to the angle to get the angle in standard position: \(\theta_{standard} = \theta + \pi\)

Step 5 :Round the answer to 4 decimal places: \(\boxed{3.4199}\)

From Solvely APP
Source: https://solvelyapp.com/problems/41787/

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