For each angle below, determine the quadrant in which the terminal side of the angle is found and find the corresponding reference angle 𝜃¯ .

Question

1. theta= -1pi/3 is found in quadrant ____ and 𝜃¯ = _______
2. theta= -1pi/4 is found in quadrant ____ and 𝜃¯ = _______
3. theta= -5pi/6 is found in quadrant ____ and 𝜃¯ = _______
4. theta= 5 is found in quadrant ____ and 𝜃¯ = _______

Answer 1

The reference angle for an angle drawn in standard position (initial side is the positive x-axis with vertex at (0,0)) is the acute angle formed by the terminal side of the angle and the x-axis.

-π/3 is in quadrant 4 with reference angle π/3

-π/4 is in quadrant 4 with reference angle π/4

-5π/6 is in quadrant 3 with reference angle π/6

5 (radians) is in quadrant 4 with reference angle 2π - 5 ≈ 1.28

Answer 2

These formulas are in radians.

1. θ=-pi/3=-180/3=-60; 4th quad
2. θ=-45º 4th
3. θ=-5pi/6=-900/6=-150º 3rd
4. θ=5º 1st