Calculate any trigonometric function including sin, cos, tan, and their inverses. Supports degrees, radians, and gradians with unit circle visualization.
Sine
0.500000
Exact: 1/2
Sine
Ratio of opposite side to hypotenuse
sin(x) = opposite / hypotenuse
Domain: All real numbers
Range: [-1, 1]
Enter angle in degrees
sin
0.500000
cos
0.866025
tan
0.577350
csc (1/sin)
2.000000
sec (1/cos)
1.154701
cot (1/tan)
1.732051
Amplitude
1
Period
2pi
Phase Shift
0
Vertical Shift
0
Equation:
y = sin((x))
sin^2(x) + cos^2(x) = 1
The fundamental trigonometric identity
1 + tan^2(x) = sec^2(x)
Derived by dividing the basic identity by cos^2(x)
1 + cot^2(x) = csc^2(x)
Derived by dividing the basic identity by sin^2(x)
csc(x) = 1 / sin(x)
sec(x) = 1 / cos(x)
cot(x) = 1 / tan(x) = cos(x) / sin(x)
tan(x) = sin(x) / cos(x)
sin(2x) = 2sin(x)cos(x)
cos(2x) = cos^2(x) - sin^2(x) = 2cos^2(x) - 1 = 1 - 2sin^2(x)
tan(2x) = 2tan(x) / (1 - tan^2(x))
Quadrant 1
All positive (0 to 90)
Quadrant 2
Sin positive (90 to 180)
Quadrant 3
Tan positive (180 to 270)
Quadrant 4
Cos positive (270 to 360)
Remember: All Students Take Calculus - All positive in Q1, Sine in Q2, Tangent in Q3, Cosine in Q4.
| Degrees | Radians | sin | cos | tan |
|---|---|---|---|---|
| 0 | 0 | 0 | 1 | 0 |
| 30 | pi/6 | 1/2 | sqrt(3)/2 | sqrt(3)/3 |
| 45 | pi/4 | sqrt(2)/2 | sqrt(2)/2 | 1 |
| 60 | pi/3 | sqrt(3)/2 | 1/2 | sqrt(3) |
| 90 | pi/2 | 1 | 0 | undefined |
| 120 | 2pi/3 | sqrt(3)/2 | -1/2 | -sqrt(3) |
| 135 | 3pi/4 | sqrt(2)/2 | -sqrt(2)/2 | -1 |
| 150 | 5pi/6 | 1/2 | -sqrt(3)/2 | -sqrt(3)/3 |
| 180 | pi | 0 | -1 | 0 |
Sine
0.500000
Exact: 1/2
Quick-start with common scenarios
Test your skills with practice problems
Practice with 3 problems to test your understanding.
Trigonometric functions relate angles to ratios of sides in a right triangle. The six basic functions are: sin (opposite/hypotenuse), cos (adjacent/hypotenuse), tan (opposite/adjacent), and their reciprocals csc, sec, cot. Use inverse functions (arcsin, arccos, arctan) to find angles from ratios. The unit circle shows all values for angles 0-360 degrees.
Trigonometry is the branch of mathematics dealing with the relationships between angles and sides of triangles. The six trigonometric functions (sine, cosine, tangent, cosecant, secant, cotangent) are fundamental to geometry, physics, engineering, and many other fields. This calculator evaluates any trig function in degrees, radians, or gradians.
In a right triangle: sin(angle) = opposite/hypotenuse, cos(angle) = adjacent/hypotenuse, tan(angle) = opposite/adjacent. Sine measures vertical displacement on the unit circle, cosine measures horizontal displacement, and tangent is their ratio.
To convert degrees to radians: multiply by pi/180. To convert radians to degrees: multiply by 180/pi. For example, 90 = 90 x (pi/180) = pi/2 radians. Remember: 360 = 2pi radians.
Inverse trig functions (arcsin, arccos, arctan) return the angle when given a ratio. For example, arcsin(0.5) = 30 because sin(30) = 0.5. They have restricted ranges to ensure unique outputs.
The unit circle is a circle with radius 1 centered at the origin. For any angle, the x-coordinate of the point on the circle equals cos(angle) and the y-coordinate equals sin(angle). It visualizes all trig values.
tan = sin/cos. At 90 and 270 degrees, cos equals 0, making tan undefined (division by zero). On a graph, these appear as vertical asymptotes where the function approaches positive or negative infinity.
Last updated: 2025-01-15
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Sine
0.500000
Exact: 1/2