Write the equation x+y=5 in normal form to find (cosØ, sinØ)

Question

A.    (√2/2, - √2/2)

B.  (√2/2,  √2/2)

C. (-√2/2,  √2/2)

 

D. (- √2/2, -√2/2)ØØ

Answer 1

graph the equation x+y=5 and it forms an isosceles right triangle

the equation is xcosα+ysinα=p where p is the perpendicular distance from the origin to the straight line whose equation is x+y=5

using the Pythagorean Theorem you can find p

5^2+5^2=x^2 where x=hypotenuse

25+25=x^2

50=x^2

x=√50=5√2 (or if you know the fact that in an isosceles right triangle the hypotenuse is a side times √2, you get 5√2)

take half of 5√2 to get 5√2/2

5^2-(5√2/2)^2=p^2

25-50/4=p^2

25-25/2=p^2

12.5=p^2

p=√12.5

the angle α is 45º because you have an isosceles right triangle and the perpendicular from the origin to the line bisects the 90º angle

xcos45º+ysin45º=√12.5

cos45º=sin45º=√2/2

B. (√2/2,√2/2)