From euler’s relation eiθ = cosθ + isinθ,

(a) use series expansions to prove that cosθ = (eiθ+e-iθ)/2, and sinθ = (eiθ−e-iθ)/2i. (b) draw the appropriate diagrams to interpret these formulas geometrically.

-22

times both sides by 2, times () by 8, add alile terms, move terms, add alike and caculate divide both sides by 3

the formula for the equation of a circle is (x – h)2+ (y – k)2 = r2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle. if a circle is tangent to the x-axis at (3,0), this means it touches the x-axis at that point.

8+10

step-by-step explanation:

you multiply 4 by 2 and 5 by 2