Definitions: Trigonometric functions relate the angles of a right triangle to the ratios of its sides. The three primary ones are:
- sin(θ) = opposite / hypotenuse
- cos(θ) = adjacent / hypotenuse
- tan(θ) = opposite / adjacent
sin = sine (ES: seno, FR:
sinus)
cos = cosine (ES: coseno, FR:
cosinus)
tan = tangent (ES/FR:
tangente)
SOH-CAH-TOA → sin=opp/hyp • cos=adj/hyp • tan=opp/adj
Intent: Fast visual reference for sin, cos, tan: solver, unit circle cues, special angles, and key identities.
Enter 2 inputs (angle+side or two sides). We'll
compute the rest.
Formulas
SOH sinθ = a / c
CAH cosθ = b / c
TOA tanθ = a / b
Deg↔Rad:
- rad = deg·π/180
- deg = rad·180/π
- rad = deg·π/180
- deg = rad·180/π
Pythagoras: c² = a² + b²
Results
a =
b =
c =
sinθ =
cosθ =
tanθ =
θ ≈
φ ≈
(φ = 90° − θ)
Each position means : angle in radian / angle in degrees (ie: π/4 |
45°). COS and SIN coordinates as follow [cos,sin].
Unit circle values (exact):
deg
rad
rad
sin
cos
tan
0°
0
0
0
1
0
30°
π/6
π/6
1/2
√3/2
1/√3
45°
π/4
π/4
√2/2
√2/2
1
60°
π/3
π/3
√3/2
1/2
√3
90°
π/2
π/2
1
0
—
120°
2π/3
2π/3
√3/2
−1/2
−√3
210°
7π/6
7π/6
−1/2
−√3/2
1/√3
310°
31π/18
31π/18
−√3/2
1/2
−√3
Not-so-basic
Formulas
Reciprocals:
csc(θ) = 1/sin(θ) = c/a — cosecant
sec(θ) = 1/cos(θ) = c/b — secant
cot(θ) = 1/tan(θ) = b/a — cotangent
csc(θ) = 1/sin(θ) = c/a — cosecant
sec(θ) = 1/cos(θ) = c/b — secant
cot(θ) = 1/tan(θ) = b/a — cotangent
Pythagorean: sin²(θ) + cos²(θ) = 1;
1 + tan²(θ) = sec²(θ); 1 + cot²(θ) = csc²(θ)
1 + tan²(θ) = sec²(θ); 1 + cot²(θ) = csc²(θ)
Cofunction: sin(90° − x) = cos(x); tan(90° − x) =
cot(x)
Angle addition: sin(α ± β) = sin(α).cos(β) ±
cos(α).sin(β);
cos(α ± β) = cos(α).cos(β) ∓ sin(α).sin(β);
tan(α ± β) = (tan(α) ± tan(β)) / (1 ∓ tan(α).tan(β))
cos(α ± β) = cos(α).cos(β) ∓ sin(α).sin(β);
tan(α ± β) = (tan(α) ± tan(β)) / (1 ∓ tan(α).tan(β))
Inverse trig (right triangle)
Formulas
θ = arcsin(a/c) = arccos(b/c) = arctan(a/b)