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
9.8 meters divided by .14 meter pieces. 70 pieces that Ralph can cut from the spool.
Answer:
A) $14/hr B) Austin
Step-by-step explanation:
A)
If he earns $140 in 10 hours you can divide 140 by 10 to find out how much he makes per hour
B)
Sarah makes $13/hr which is $1 less than Austin
Answer: 42 - 8x
Step-by-step explanation:
Here is the complete question:
Jessica had $15. She bought 3 apples for x dollars each. Levi had $27 and bought 5 apples for x dollars each. Which expression represents how much money both Jessica and Levi have left altogether?
Select one:
27 – 5x
42 – 8x
12 – 2x
39 – 3x
From the question, Jessica had $15. She bought 3 apples for x dollars each. This means she had:
15 - (3 × x) = 15 - 3x
Levi had $27 and bought 5 apples for x dollars each. Levi will have:
27 - (5 × x) = 27 - 5x
The amount they'll have altogether will be the addition of their amount left. This will be:
15 - 3x + 27 - 5x
= 15 + 27 - 3x - 5x
= 42 - 8x
Answer:
158.33 minutes = 2.63 hours
Step-by-step explanation:
