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AleksandrR [38]
2 years ago
10

In a unit circle, ø = 2pi radians What is the terminal point?

Mathematics
1 answer:
BlackZzzverrR [31]2 years ago
5 0

Answer:

The terminal point is (1, 0) ⇒ D

Step-by-step explanation:

In the unit circle, Ф is the angle between the terminal side and the positive part of the x-xis.

  • The terminal point on the positive part of the x-axis is (1, 0),which means Ф = 0° or 360° and cosФ = 1, sinФ = 0
  • The terminal point on the positive part of the y-axis is (0, 1),which means Ф = 90° and cosФ = 0, sinФ = 1
  • The terminal point on the negative part of the x-axis is (-1, 0),which means Ф = 180° and cosФ = -1, sinФ = 0
  • The terminal point on the negative part of the y-axis is (0, -1),which means Ф = 270° and cosФ = 0, sinФ = -1

In a unit circle

∵ Ф = 2π radians

∵ 2π radians = 360°

→ By using the 1st rule above

∴ The terminal point is (1, 0)

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Answer:

sum is 125,500

sum in summation notation is \sum\limits_{n=0}^n a+nd= (2a+(n-1)d)n/2

Step-by-step explanation:

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_____________________________________________________

in the problem

series is multiple of 4 starting from 4 ending at 1000

so series will look like

series: 0,4,8,12,16..................1000

a is first term so

here a is 0

lets find d the common difference

common difference is given by nth term - (n-1)th term

lets take nth term as 8

so (n-1)th term = 4

Thus,

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d  can also be seen 4 intuitively as series is multiple of four.

_____________________________________________

let calculate value of n

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Nth term can be described

Nth term = 0+(n-1)d

1000 =   (n-1)4

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_____________________________________

now we have

n = 1000

a = 0

d = 4

so we can calculate sum of the series by using formula given above

sum = (2a+(n-1)d)n/2

       = (2*0 + (251-1)4)251/2

       = (250*4)251/2

     = 1000*251/2 = 500*251 = 125,500

Thus, sum is 125,500

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