Question

if theta is in standard position and its terminal side passes through the point (-3,2) find the value of cos theta to the nearest degree

Answer 1

Imagine a triangle with a one leg 3 units in the -x direction and another leg 2 units in the + y direction. Theta is defined as the angle between the two legs. Since we know that cos of an angle is equivalent to the adjacent leg divided by the hypothenuse,

cos(theta) = \[-3/\sqrt{(-3)^2 + (2)^2}\]

where the numerator value is the length of the adjacent leg and the denominator value is the length of the hypothenuse.