Calculate the sum of two or more angles in degrees or radians and get the total in radians plus sin, cos, and tan of the combined angle.
Angle Addition Formula
The calculator first converts every entered angle to radians, adds the angles, then evaluates the sine, cosine, and tangent of the total angle.
\theta_{\text{rad}} = \theta_{\text{deg}} \cdot \frac{\pi}{180}S = \theta_1 + \theta_2 + \theta_3 + \cdots + \theta_n
\sin(S),\quad \cos(S),\quad \tan(S)
- \(\theta_{\text{deg}}\) = an angle entered in degrees
- \(\theta_{\text{rad}}\) = the same angle converted to radians
- \(\theta_1, \theta_2, \theta_3, \ldots, \theta_n\) = each angle after conversion to radians if needed
- \(S\) = total angle sum in radians
- \(\sin(S)\) = sine of the total angle
- \(\cos(S)\) = cosine of the total angle
- \(\tan(S)\) = tangent of the total angle
If you enter an angle in degrees, it is converted to radians before addition. If you enter an angle in radians, it is added directly. After the total angle is found, the calculator returns the sum in radians along with the sine, cosine, and tangent of that sum.
Common Angle Conversions and Trig Values
Use these values to check common results when adding angles.
| Degrees | Radians | Decimal Radians |
|---|---|---|
| 0° | 0 | 0.0000 |
| 30° | π/6 | 0.5236 |
| 45° | π/4 | 0.7854 |
| 60° | π/3 | 1.0472 |
| 90° | π/2 | 1.5708 |
| 180° | π | 3.1416 |
| 360° | 2π | 6.2832 |
| Total Angle | Radians | sin | cos | tan |
|---|---|---|---|---|
| 30° | 0.5236 | 0.5000 | 0.8660 | 0.5774 |
| 45° | 0.7854 | 0.7071 | 0.7071 | 1.0000 |
| 90° | 1.5708 | 1.0000 | 0.0000 | Undefined |
| 180° | 3.1416 | 0.0000 | -1.0000 | 0.0000 |
Example Section
Example 1: Add two angles in degrees
Add 30° and 45°.
30^\circ = 30 \cdot \frac{\pi}{180} = 0.523645^\circ = 45 \cdot \frac{\pi}{180} = 0.7854S = 0.5236 + 0.7854 = 1.3090
The angle sum is 1.3090 radians. The trig values are approximately sin(S) = 0.9659, cos(S) = 0.2588, and tan(S) = 3.7321.
Example 2: Add one degree angle and one radian angle
Add 90° and 0.5 radians.
90^\circ = 90 \cdot \frac{\pi}{180} = 1.5708S = 1.5708 + 0.5 = 2.0708
The angle sum is 2.0708 radians. The trig values are approximately sin(S) = 0.8776, cos(S) = -0.4794, and tan(S) = -1.8305.
FAQ Section
Can you add angles measured in degrees and radians together?
Yes, but they must use the same unit before addition. This calculator converts degree inputs to radians, leaves radian inputs unchanged, and then adds all angles in radians.
Why is the angle sum shown in radians?
Radians are the standard unit used by most trigonometric calculations. Since sine, cosine, and tangent are evaluated from the total angle in radians, the calculator displays the summed angle in radians.
Why can tangent be very large or undefined?
Tangent is calculated as sin(S) divided by cos(S). When cos(S) is very close to 0, tangent becomes very large. At angles such as π/2 radians, or 90°, tangent is undefined because division by zero is not possible.
