What are the components of the vector between the origin and the polar coordinate $(1, \frac{5 π}{4})$ $(1, (5pi)/4)$ ?

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What are the components of the vector between the origin and the polar coordinate $(1, \frac{5 π}{4})$ $(1, (5pi)/4)$ ?

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Answer 1 · 2016-01-15T20:39:21

The $x$ $x$ component is: $cos (\frac{5 π}{4})$ $cos((5pi)/4)$
The $y$ $y$ component is: $sin (\frac{5 π}{4})$ $sin((5pi)/4)$

Explanation:

Remembering our trigonometry, the vertical component of a vector is given by
$r \cdot sin (θ)$ $r*sin(theta)$ where $r$ $r$ is the length of the line,
and the horizontal component by
$r \cdot cos (θ)$ $r*cos(theta)$

![https://en.wikipedia.org/wiki/Trigonometry]( useruploads.socratic.org )

in the polar coordinate $(1, \frac{5 π}{4})$ $(1,(5pi)/4)$ , $r$ $r$ is 1, and the angle $θ = \frac{5 π}{4}$ $theta = (5pi)/4$ .

Hence:
The $x$ $x$ component is: $cos (\frac{5 π}{4})$ $cos((5pi)/4)$
The $y$ $y$ component is: $sin (\frac{5 π}{4})$ $sin((5pi)/4)$

In this case, $\frac{5 π}{4}$ $(5pi)/4$ is midway in the lower left quadrant, or $135^{\circ}$ $135^@$ , so both are equal to $- \frac{1}{\sqrt{2}}$ $-1/sqrt2$

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What are the components of the vector between the origin and the polar coordinate $(1, \frac{5 π}{4})$ $(1, (5pi)/4)$ ?

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Explanation:

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What are the components of the vector between the origin and the polar coordinate $(1, \frac{5 π}{4})$ $(1, (5pi)/4)$ ?