How do you write in simplest radical form the coordinates of point A if A is on the terminal side of angle in standard position whose degree measure is $θ$ $theta$ : OA=15, $θ = 135^{\circ}$ $theta=135^circ$ ?

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How do you write in simplest radical form the coordinates of point A if A is on the terminal side of angle in standard position whose degree measure is $θ$ $theta$ : OA=15, $θ = 135^{\circ}$ $theta=135^circ$ ?

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Answer 1 · 2017-11-17T06:03:27

The coordinates are $(\frac{15}{\sqrt{2}}, \frac{15}{\sqrt{2}})$ $(15/sqrt(2),15/sqrt(2))$

Explanation:

Start by making a reference triangle for your angle.

![Desmos.com and MS Paint](useruploads.socratic.org)

The inner angle of the right triangle is $180 - 135 = 45$ $180-135=45$ degrees. The side opposite the $45$ $45$ degree angle is the $y$ $y$ coordinate, and the side adjacent to the $45$ $45$ degree angle is the $x$ $x$ coordinate.

The properties of a $45 - 45 - 90$ $45-45-90$ right triangle are

![Dummies.com](useruploads.socratic.org)

So the hypotenuse is $15 = y \sqrt{2}$ $15=ysqrt(2)$ . We can solve this by dividing both sides by $\sqrt{2}$ $sqrt(2)$ .

$x = \frac{15}{\sqrt{2}}$ $x=15/sqrt(2)$ and $y = \frac{15}{\sqrt{2}}$ $y=15/sqrt(2)$ .

Thus, the coordinates are $(\frac{15}{\sqrt{2}}, \frac{15}{\sqrt{2}})$ $(15/sqrt(2),15/sqrt(2))$

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How do you write in simplest radical form the coordinates of point A if A is on the terminal side of angle in standard position whose degree measure is $θ$ $theta$ : OA=15, $θ = 135^{\circ}$ $theta=135^circ$ ?

1 Answer

Explanation:

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How do you write in simplest radical form the coordinates of point A if A is on the terminal side of angle in standard position whose degree measure is θtheta: OA=15, θ=135∘theta=135^circ?

1 Answer

Explanation:

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How do you write in simplest radical form the coordinates of point A if A is on the terminal side of angle in standard position whose degree measure is $θ$ $theta$ : OA=15, $θ = 135^{\circ}$ $theta=135^circ$ ?