Answered: -2, 4 ): quadrant

Trigonometry (MindTap Course List)

8th Edition

ISBN:9781305652224

Author:Charles P. McKeague, Mark D. Turner

Publisher:Charles P. McKeague, Mark D. Turner

Chapter5: Identities And Formulas

Section5.4: Half-angle Formulas

Problem 11PS: If 180A270, then A/2 terminates in which quadrant?

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For the point with the given polar coordinates in determine the quadrant in which the point lies if it is graphed in a rectangular coordinate system.

System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

Expert Solution

Step 1

Given point in polar coordinate is $(- 2, - \frac{π}{4})$ .

We know that points in the polar coordinates is given as $(r, θ)$ .

So, $r = - 2 & θ = - \frac{π}{4}$

Now, coordinates in rectangular coordinate is given as $x = r \cos θ & y = r \sin θ$

Therefore,

$\begin{array}{rcl} x & = & r \cos θ \\ = & (- 2) \cos (- \frac{π}{4}) \\ = & - 2 \cos (\frac{π}{4}) (S i n c e, \cos (- θ) = \cos θ) \\ = & - 2 \cdot \frac{1}{\sqrt{2}} \\ = & - \sqrt{2} \end{array}$

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