At 358°, this is a reflex angle, which goes more than halfway around a circle. It is the "outside" of a 2° angle: together they make a full 360° circle.
358° is 179/180 of a full circle, or 179π/90 radians. If you face north and turn 358° clockwise, you end up facing between NNW and N (closest to north (N)).
358° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 2° |
| Radians | 179π/90 ≈ 6.248279 |
| Gradians | 397.7778 grad |
| Fraction of a turn | 179/180 (99.44%) |
| Degrees, minutes, seconds | 358° 0′ 0″ |
| Compass bearing | between NNW and N (closest to north (N)) |
Trigonometric values of 358°
| Function | Value |
|---|---|
| sin 358° | −0.034899 |
| cos 358° | 0.999391 |
| tan 358° | −0.034921 |
358° on a protractor
How to draw a 358° angle with a protractor
- Subtract from 360°: 360° − 358° = 2°. 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 2°.
- Join the vertex to the dot. The inside angle is 2°; the outside angle, going the long way around, is 358°. Draw the angle arc on the outside and label it 358°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 358° directly.
Drawing it a 358° 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 0.35 inches (about 3/8″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 2°, because tan 2° ≈ 0.0349.
- That gives you 2°. The outside (reflex) angle is 358°.
Where you see 358° angles
- The Earth turns 358° on its axis in about 23 h 52 min.
- A 358° 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
358° angle FAQ
What type of angle is 358°?
A 358° angle is a reflex angle, because it is between 180° and 360°.
Does a 358° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 358° is already larger than both. What it does have is an explement (conjugate) of 2°, the angle that completes a full 360° circle.
How many radians is 358 degrees?
358° = 179π/90 radians ≈ 6.2483 rad. To convert degrees to radians, multiply by π/180: 358 × π/180 = 179π/90.
How do I measure a 358° angle on my screen?
Open the online protractor with 358° preset, or type 358 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
