Answer:
1) If we have a point (x, y), the angle between the x-axis and a ray that goes from the origin to the point is defined by:
cos(θ) = x/(√(x^2 + y^2))
sin(θ) = y/(√(x^2 + y^2))
Then for the point:
(√(7)/4 , 3/4)
x = √(7)/4
y = 3/4
√(x^2 + y^2) = √((√(7)/4)^2 + ( 3/4)^2) = (1/4)*√(7 + 9) = 1
Then replacing these values in the above equations for the cosine and sine functions, we get:
cos(θ) = x/(√(x^2 + y^2)) = (√(7)/4)/1 = √(7)/4
sin(θ) = y/(√(x^2 + y^2)) = (3/4)/1 = 3/4
2) To find the period, we just need to find the distance between two peaks, or two x-intersects (such that the slope is the same).
Let's look at the graph.
We can see that at x = 0, the graph intersects the x-axis and increases
The next point where this happens is at x = π/3
Then the period of this function is:
P = π/3 - 0 = π/3
The period is π/3