Match the following vocabulary

Mathematics

1 answer:

stiks02 [169]2 years ago

5 0

The properties of a Circle with their definitions are; As highlighted below

<h3>How to identify Properties of a Circle?</h3>

1) The distance around a circle is called; Circumference

2) A portion of the circumference of a circle is called; Arc Length

3) The distance from the center to any point on a circle is called; Radius.

4) The distance through the center between points on a circle is called; Diameter

5) The degree measurement of an arc (in reference to its central

angle) is called; Arc Measure

6) An arc which measures less than 180° is called; Minor arc

7) An arc which measures exactly 180° is called; Semi Circle

Read more about Properties of a Circle at; brainly.com/question/17072060

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Convert the polar coordinates (-3, -60°) to Cartesian coordinates.

notsponge [240]

Answer:

(1.5,-2.6)

Step-by-step explanation:

Given the polar coordinates (-3,60°).

Let our Cartesian coordinates be (x,y)

#We know that when converting the rectangular coordinates (x,y) to polar (r,θ), then:

$r=\sqrt{x^2+y^2}\\\\\therefore r^2=x^2+y^2\\\\\theta=tan^{-1}(y/x)\\\therefore tan \theta=y/x$

#Using the illustration above, we can express our polar coordinates as:

$-3=\sqrt{x^2+y^2}\\\\-60\textdegree=tan^{-1}(y/x}$

#Solve simultaneously to solve for x and y:

$(-3)^2=x^2+y^2\ \ \ \ \ \ \ \ \ \ i\\\\tan(-0\texdegree)=y/x\ \ \ \ \ \ \ \ ...ii\\\\y=x\ tan(-60\textdegree)\ \ \ \ \ \ \ ...iii\\\\\#substitute\ y \ in\ i\\\\(-3)^2=x^2+(x \ tan (-60\textdegree))^2\\\\9=x^2+3x^2\\\\x=\sqrt{9/4}=1.5\\\\y=1.5\ tan(-60\textdegree)=-2.5981\approx-2.6$