The terminal side of an angle...

Question

The terminal side of an angle θ contains the point (√2, √2) in standard position. Determine the following:

 

 

a. What is the radius length of the circle? 

 

b. What is the angle measure in both degrees and radians?

Answer 1

The given coordinate is the endpoint of a vector from the origin (0, 0).

 

We can use the distance formula to find the radius.

 

r = √(x² + y²)

r = √[√(2)√(2) + √(2)√(2)]

r = √(2 + 2)

r = √(4)

r = 2

 

 

To find the angle, we can use the inverse tangent of y coordinate over the x coordinate.

 

θ = tan^-1(√2 / √2)

θ = tan^-1(1)

θ = 45°

θ = π/4