Answer:
Part 1:
radians
Part 2: The minute hand travels
inches.
Part 3: The minute hand travels
radians.
Part 4: The coordinate point is ![(-\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2})](https://tex.z-dn.net/?f=%28-%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%2C%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%29)
Step-by-step explanation:
<u>Part 1:</u>
There are 60 minutes in an hour. 1 hour is 1 revolution (1 circle), which is 360°.
So each minute represents
degrees
From 3:35 to 3:55 is 20 minutes. Hence, 20 minutes is
degrees.
<u><em>To convert from degrees to radians, we multiply the degrees by
</em></u>
120° is equal to
radians
<u>Part 2:</u>
We want to find the "arc length" of this.
Formula for arc length is ![s=r\theta](https://tex.z-dn.net/?f=s%3Dr%5Ctheta)
Where,
- s is the arc length
- r is the radius (here the minute hand was given as 4 inches)
is the angle in radians (we found it to be
)
So, ![s=r\theta\\s=(4)(\frac{2\pi }{3})=\frac{8\pi}{3}](https://tex.z-dn.net/?f=s%3Dr%5Ctheta%5C%5Cs%3D%284%29%28%5Cfrac%7B2%5Cpi%20%7D%7B3%7D%29%3D%5Cfrac%7B8%5Cpi%7D%7B3%7D)
The minute hand travels
inches.
<u>Part 3:</u>
Here we use the arc length formula where we want to find
given that
and radius is 4 inches. So we have:
![s=r\theta\\3\pi=(4)(\theta)\\\theta=\frac{3\pi}{4}](https://tex.z-dn.net/?f=s%3Dr%5Ctheta%5C%5C3%5Cpi%3D%284%29%28%5Ctheta%29%5C%5C%5Ctheta%3D%5Cfrac%7B3%5Cpi%7D%7B4%7D)
The minute hand travels
radians.
<u>Part 4:</u>
The coordinate point associated with a specif radian is given by the formula:
![(x,y)=(cos(\theta)sin(\theta))\\(x,y)=(cos(\frac{3\pi}{4})sin(\frac{3\pi}{4}))\\(x,y)=(-\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2})](https://tex.z-dn.net/?f=%28x%2Cy%29%3D%28cos%28%5Ctheta%29sin%28%5Ctheta%29%29%5C%5C%28x%2Cy%29%3D%28cos%28%5Cfrac%7B3%5Cpi%7D%7B4%7D%29sin%28%5Cfrac%7B3%5Cpi%7D%7B4%7D%29%29%5C%5C%28x%2Cy%29%3D%28-%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%2C%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%29)
Thus the coordinate point is ![(-\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2})](https://tex.z-dn.net/?f=%28-%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%2C%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%29)