Can pie be written as a natural number
1 answer:
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Answer:
-1
Step-by-step explanation:
See the attachment for the polynomial long division. The constant in the quotient is -1.
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Here, there is a remainder of -x. If there were no remainder the constant in the quotient is the ratio of the constant in the dividend to the constant in the divisor: -2/2 = -1.
That could be a first guess in a "guess and check" solution approach.
<em>Guess</em>: first term of binomial quotient is (2x^3)/x^2 = 2x; last term of binomial quotient is -2/2 = -1. So, the quotient is guessed to be (2x -1).
<em>Check</em>: (2x -1)(x^2 -x +2) = 2x^3 -3x^2 +5x -2
Subtracting this from the actual dividend gives a remainder of -x. This has a lower degree than the divisor, so no further adjustment of the quotient is required.
Now, there are 360° in a circle, how many times does 360° go into 1860°?
well, let's check that,
now, this is a negative angle, so it's going clockwise, like a clock moves, so it goes around the circle clockwise 5 times fully, and then it goes 1/6 extra.
well, we know 360° is in a circle, how many degrees in 1/6 of 360°? well, is just 360/6 or their product, and that's just 60°.
so -1860, is an angle that goes clockwise, negative, 5 times fully, then goes an extra 60° passed.
5 times fully will land you back at the 0 location, if you move further down 60° clockwise, that'll land you on the IV quadrant, with an angle of -60°.
therefore, the csc(-1860°) is the same as the angle of csc(-60°), which is the same as the csc(360° - 60°) or csc(300°).
well, let's check that,
now, this is a negative angle, so it's going clockwise, like a clock moves, so it goes around the circle clockwise 5 times fully, and then it goes 1/6 extra.
well, we know 360° is in a circle, how many degrees in 1/6 of 360°? well, is just 360/6 or their product, and that's just 60°.
so -1860, is an angle that goes clockwise, negative, 5 times fully, then goes an extra 60° passed.
5 times fully will land you back at the 0 location, if you move further down 60° clockwise, that'll land you on the IV quadrant, with an angle of -60°.
therefore, the csc(-1860°) is the same as the angle of csc(-60°), which is the same as the csc(360° - 60°) or csc(300°).