Special Angles in Quadrant II
Be forewarned: this involves lots of flipping (numbers, not burgers).
Let's look at our 45°-45°-90°and 30°-60°-90° references triangles again. This time, let's flip them to Quadrant II:
For the 45°-45°-90° triangle, ɵ = 135° and ρ = 45°.
For this 30°-60°-90° triangle, ɵ = 120° and ρ = 60°.
For this 30°-60°-90° triangle, ɵ = 150° and ρ = 30°.
Special Angles in Quadrant III
Now, flip your triangles over into Quadrant III.
For the 45°-45°-90° triangle, ɵ = 225° and ρ = 45°.
For this 30°-60°-90° triangle, ɵ = 210° and ρ = 30°.
For this 30°-60°-90° triangle, ɵ = 240° and ρ = 60°.
Special Angles in Quadrant IV
Flip your triangles over into Quadrant IV for the grand finale.
For the 45°-45°-90° triangle, ɵ = 315° and ρ = 45°.
For this 30°-60°-90° triangle, ɵ = 300° and ρ = 60°.
For this 30°-60°-90° triangle, ɵ = 330° and ρ = 30°.