The point P(-4,2) is a point on the terminal arm of an angle theta in standard position

Question

a) state the exact value of cos theta

b) calculate theta to the nearest degree

Answer 1

Let P, our point, be equivalent to (x, y) letting x= -4 and y = 2

Let r be the length of the line segment drawn from the origin to the point given

r = sqrt ( x^2 + y^2)

r = sqrt ( (-4)^2 +(2)^2 ) = sqrt( 16+4) = sqrt(20) = sqrt(4*5)= 2sqrt(5)

sin(theta) = y/r = 2/ (2sqrt(5)) = 1/sqrt(5)

cos(theta) = x/r = -4/ 2*sqrt(5) = -2/sqrt(5) or -2* 1/sqrt(5) ---- exact value

To convert the sector to degrees, multiply by 360* of a circle

-2 / sqrt(5) * 360 = -321.9937* = -322*