Quick start
- Type the angle, for example 135.
- Choose degrees or radians.
- Read sin, cos, tan, csc, sec and cot, with the quadrant and reference angle.
Exact values worth knowing
| Angle | sin | cos | tan |
|---|---|---|---|
| 0° | 0 | 1 | 0 |
| 30° | 1/2 | √3/2 | √3/3 |
| 45° | √2/2 | √2/2 | 1 |
| 60° | √3/2 | 1/2 | √3 |
| 90° | 1 | 0 | undefined |
Angles past 90°
Find the reference angle, the acute angle to the x-axis, and then fix the sign by quadrant. 135° is in the second quadrant with a reference angle of 45°. Sine is positive there and cosine is negative, so sin 135° = √2/2 and cos 135° = −√2/2.
The reciprocal functions
csc = 1 ÷ sin, sec = 1 ÷ cos and cot = 1 ÷ tan. They are undefined wherever the function underneath is 0.
Degrees and radians
A full turn is 360° or 2π radians. To convert degrees to radians, multiply by π/180. 135° = 3π/4.
Common questions
Why is tan 90° undefined?
tan = sin ÷ cos, and cos 90° = 0. Dividing by zero is undefined.
Which quadrants make each function positive?
All in the first, sine in the second, tangent in the third and cosine in the fourth.
Can I enter negative angles?
Yes. −30° is the same position as 330°.