Understanding Trigonometric Functions
Trigonometric functions relate angles to ratios of sides in a right triangle. They are fundamental to mathematics, physics, engineering, and signal processing. The six basic trig functions are sine, cosine, tangent, and their reciprocals: cosecant, secant, and cotangent.
The Six Trig Functions
Sine (sin)
Ratio of the opposite side to the hypotenuse.
sin(theta) = opposite / hypotenuse
Cosine (cos)
Ratio of the adjacent side to the hypotenuse.
cos(theta) = adjacent / hypotenuse
Tangent (tan)
Ratio of the opposite side to the adjacent side.
tan(theta) = opposite / adjacent
Cosecant (csc)
Reciprocal of sine.
csc(theta) = 1 / sin(theta)
Secant (sec)
Reciprocal of cosine.
sec(theta) = 1 / cos(theta)
Cotangent (cot)
Reciprocal of tangent.
cot(theta) = 1 / tan(theta)
Angle Units
Angles can be measured in degrees (360 per full rotation), radians (2pi per full rotation), or gradians (400 per full rotation). This calculator supports all three units and converts between them automatically.
Key Values to Remember
- sin(30) = 0.5, cos(30) = sqrt(3)/2, tan(30) = 1/sqrt(3)
- sin(45) = cos(45) = sqrt(2)/2, tan(45) = 1
- sin(60) = sqrt(3)/2, cos(60) = 0.5, tan(60) = sqrt(3)
- sin(90) = 1, cos(90) = 0, tan(90) = undefined