Question

let P be a point in Q1 such that the slope of the line connecting P to the origin is sq. root of 2 and the distance from P to the origin is 3 units. Find the coordinates of P, state all trig values for angle formed by the line and the positive x-axis, and the measure of said angle rounded to the nearest minute.

Answer 1

If the slope is √2 then y = √2 x
So, if the angle is z, then tan z = √2. That will give you all the other values; just draw a triangle with legs x=1, y=√2, hypot = √3

Now, to find point P:

Since x^2 + y^2 = 9,

x^2 + 2x^2 = 9
3x^2 = 9
x^2 = 3
x = √3
y = √6

P=(√3,√6)