For the given central angle, determine the distance traveled along the unit circle from the point (1, 0).

Mathematics

1 answer:

viva [34]2 years ago

3 0

9514 1404 393

Answer:

b. 6.28 units

Step-by-step explanation:

The travel through 360° takes you around the full circumference of the circle. That circumference is ...

C = 2πr

Since this is a unit circle, the radius is 1, so the circumference is ...

C = 2π·1 = 2π ≈ 6.28 . . . units (counterclockwise)

Angles are generally considered to be positive in the counterclockwise direction, so the distance traveled is 6.28 units counterclockwise. Answer choice (a) has the correct number of units, but the direction is incorrect.

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dimaraw [331]

Midpoint formula is $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$ .

So starting with this one, we will be solving for the coordinates of the unknown endpoint separately. Starting with the x-coordinate, since we know that the midpoint x-coordinate is 5 and the x-coordinate of N is 2, our equation is set up as such: $\frac{x+2}{2}=5$ From here we can solve for the x-coordinate of Q.

Firstly, multiply both sides by 2: $x+2=10$

Next, subtract both sides by 2 and your x-coordinate is $x=8$

With finding the y-coordinate, it's a similar process as with the x-coordinate except that we are using the y-coordinates of the midpoint and endpoint N.

$\frac{y+0}{2}=2\\ y=4$