A 333° angle is a reflex angle: it is bigger than a straight line (180°) but less than a full turn (360°). It is the "outside" of a 27° angle: together they make a full 360° circle.
333° is 37/40 of a full circle, or 37π/20 radians. If you face north and turn 333° clockwise, you end up facing between NW and NNW (closest to north-northwest (NNW)).
333° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 27° |
| Radians | 37π/20 ≈ 5.811946 |
| Gradians | 370 grad |
| Fraction of a turn | 37/40 (92.5%) |
| Degrees, minutes, seconds | 333° 0′ 0″ |
| Compass bearing | between NW and NNW (closest to north-northwest (NNW)) |
Trigonometric values of 333°
| Function | Value |
|---|---|
| sin 333° | −0.45399 |
| cos 333° | 0.891007 |
| tan 333° | −0.509525 |
333° on a protractor
How to draw a 333° angle with a protractor
- Subtract from 360°: 360° − 333° = 27°. A standard protractor only goes to 180°, so you draw the smaller angle first.
- Draw a straight line with a ruler and mark the vertex at one end.
- Place the protractor's center mark on the vertex, line up the 0° baseline with your line, and make a dot at 27°.
- Join the vertex to the dot. The inside angle is 27°; the outside angle, going the long way around, is 333°. Draw the angle arc on the outside and label it 333°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 333° directly.
Drawing it a 333° angle without a protractor (rise and run method)
- Draw a straight baseline and measure exactly 10 inches along it from the vertex.
- At the 10-inch mark, draw a short line straight up at 90° (use a carpenter's square or the corner of a sheet of paper).
- Measure 5.1 inches (about 5 1/8″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 27°, because tan 27° ≈ 0.5095.
- That gives you 27°. The outside (reflex) angle is 333°.
Where you see 333° angles
- The Earth turns 333° on its axis in about 22 h 12 min.
- A 333° reflex angle is what you measure when you go the "long way" around, like the outside corner of a building or a turn of more than half a circle.
Related angles
333° angle FAQ
What type of angle is 333°?
A 333° angle is a reflex angle, because it is between 180° and 360°.
Does a 333° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 333° is already larger than both. What it does have is an explement (conjugate) of 27°, the angle that completes a full 360° circle.
How many radians is 333 degrees?
333° = 37π/20 radians ≈ 5.8119 rad. To convert degrees to radians, multiply by π/180: 333 × π/180 = 37π/20.
How do I measure a 333° angle on my screen?
Open the online protractor with 333° preset, or type 333 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
