Trigonometric Functions (sin, cos, tan)
Evaluate trigonometric expressions using sin, cos, and tan functions with the pi constant. Learn radian-based input and common angle values on the unit circle.
Trigonometry
Detailed Explanation
Trigonometric Functions in the Evaluator
The Math Expression Evaluator provides three core trigonometric functions that operate in radians (not degrees):
- sin(x) -- returns the sine of x
- cos(x) -- returns the cosine of x
- tan(x) -- returns the tangent of x
Using the pi Constant
Since most familiar angles are expressed as fractions of pi, the
built-in pi constant is essential:
sin(pi/6) = 0.5 (30 degrees)
cos(pi/3) = 0.5 (60 degrees)
tan(pi/4) = 1 (45 degrees)
sin(pi/2) = 1 (90 degrees)
cos(pi) = -1 (180 degrees)
Converting Degrees to Radians
If you think in degrees, convert first:
radians = degrees * pi / 180
For example, to compute sin(45 degrees): sin(45 * pi / 180).
Common Unit Circle Values
| Angle (deg) | Radians | sin | cos | tan |
|---|---|---|---|---|
| 0 | 0 | 0 | 1 | 0 |
| 30 | pi/6 | 0.5 | 0.866 | 0.577 |
| 45 | pi/4 | 0.707 | 0.707 | 1 |
| 60 | pi/3 | 0.866 | 0.5 | 1.732 |
| 90 | pi/2 | 1 | 0 | undefined |
Combining Trig with Other Operations
You can compose expressions freely:
sin(pi/4)^2 + cos(pi/4)^2 = 1 (Pythagorean identity)
2 * sin(pi/6) * cos(pi/6) = 0.866 (double-angle formula)
Use Case
A physics student computing projectile trajectory components using sine and cosine, or a game developer calculating rotation angles.