How do you determine the exact coordinates of a point on the terminal arm of the angle in standard position given 45 degrees?

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How do you determine the exact coordinates of a point on the terminal arm of the angle in standard position given 45 degrees?

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Answer 1 · 2018-02-26T10:20:45

See below.

Explanation:

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By looking at the diagram we can find a relationship between the Cartesian coordinates and the angular measurement.

Point $P$ $bbP$ has Carteaian coordinates $(x, y)$ $(x,y)$ , and polar coordinates $(r, θ)$ $(r,theta)$ , we are only concerned with Cartesian for this. We can see that these correspond to the sine and cosine functions in the following way.

$x = r cos (θ)$ $x=rcos(theta)$

$y = r sin (θ)$ $y=rsin(theta)$

Where $r$ $bbr$ is the radius, for a unit circle this will be $1$ $bb1$ . The cordinates of $P$ $bbP$ are now:

$(r cos (θ), r sin (θ))$ $(rcos(theta),rsin(theta))$

So using this idea:

For:

radius $1$ $bb1$ and $θ = 45^{\circ}$ $theta=45^@$ , we have:

$x = cos (45^{\circ}) = \frac{\sqrt{2}}{2}$ $x=cos(45^@)=sqrt(2)/2$

$y = sin (45^{\circ}) = \frac{\sqrt{2}}{2}$ $y= sin(45^@)=sqrt(2)/2$

So coordinates are:

$(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2})$ $(sqrt(2)/2,sqrt(2)/2)$

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How do you determine the exact coordinates of a point on the terminal arm of the angle in standard position given 45 degrees?

1 Answer

Explanation:

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