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Unit circle
A circle centered at the origin with radius 1 (i.e. this circle) is called as unit circle. The unit circle is very useful in Trigonometry.
(b) x2+ ( y - 3)2 = 4
In this part, it looks as the x coordinate of the center is zero as with the earlier part. However, this time there is something more with the y term and thus comparing this term to the standard form of the circle we can see that the y coordinate of the center have to be 3. The center & radius of this circle is then,
center = (0, 3) radius = √4 = 2
Following is a sketch of the circle. The center is marked alongwith a red cross in this graph.
1. Suppose n ≡ 7 (mod 8). Show that n ≠ x 2 + y 2 + z 2 for any x, y, z ε Z. 2. Prove ∀n ε Z, that n is divisible by 9 if and only if the sum of its digits is divisible by 9.
Verify Liouville''s formula for y^ prime prime prime -y^ prime prime - y'' + y = 0 in [0, 1]
factories Y=(B+CA)(C+A''B)
Recognizes the absolute extrema & relative extrema for the following function. f ( x ) = x 2 on [-1, 2] Solution: As this function is simpl
Solving a System of 2 Equations Using the Addition/Subtraction Method To solve a system of linear equations using the addition/subtraction method, both equations should first b
Solve sin (α /7) =0 . Solution By Using a unit circle it isn't too difficult to see that the solutions to this equation are, α /7 = 0 + 2 ? n ⇒ α = 14 ? n
1. Consider the following context free grammar G with start symbol S (we write E for the empty string, epsilon): S ---> bB | aSS A ---> aB | bAA B ---> E | bA | aS a. D
In these problems we will begin with a substance which is dissolved in a liquid. Liquid will be entering as well as leaving a holding tank. The liquid entering the tank may or may
prove angle MJL is congruent to angle KNL
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