r
sin
θ
=
−
3
Explanation:
Imagine we have a point
P
with Rectangular (also called Cartesian) coordinates
(
x
,
y
)
and Polar coordinates
(
r
,
θ
)
.
The following diagram will help us visualise the situation better:
https://keisan.casio.com/exec/system/1223526375
https://keisan.casio.com/exec/system/1223526375
We can see that a right triangle is formed with sides
x
,
y
and
r
, as well as an angle
θ
.
We have to find the relation between the Cartesian and Polar coordinates, respectively.
By Pythagora's theorem, we get the result
r
2
=
x
2
+
y
2
The only properties we can say about
θ
are its trigonometric functions:
sin
θ
=
y
/
r
⇒
y
=
r
sin
θ
cos
θ
=
x
/
r
⇒
x
=
r
cos
θ
So we have the following relations:
⎧
⎪
⎨
⎪
⎩
r
2
=
x
2
+
y
2
y
=
r
sin
θ
x
=
r
cos
θ
Now, we can see that saying
y
=
−
3
in the Rectangular system is equivalent to say
r
sin
θ
=
−
3
Answer link
Jim G.
May 19, 2018
r
=
−
3
sin
θ
Explanation:
to convert from
cartesian to polar
∙
x
x
=
r
cos
θ
and
y
=
r
sin
θ
⇒
r
sin
θ
=
−
3
⇒
r
=
−
3
sin
θ
Answer:
is it multiple choice answers ?
V of rec. prism = whl = 3x5x6 = 90
V of cone = 3.14 x (3)^2 (8) /3= 75.36
90 - 75.36 = 14.64
answer
14.64
Volume units quarts to gallons (fluid and dry) conversion factor is 0.25 (quart is 1/4 of an gallon). To find out how many gallons in quarts, multiply by the factor, or simply use the converter below.
1 Quart = 0.25 (1/4) Gallon [US, UK, Fluid or Dry]
Quart and gallon are imperial and US customary volume measurement units. In US customary system, both units have different volume capacity for dry and fluid measurements but in imperial (UK), the volume is the same for both fluid and dry measurement.
