Theta (θ) Calculator — All Six Trigonometric Functions
Enter angle θ in degrees or radians and instantly get all six trigonometric functions — sin, cos, tan, cot, sec and csc — plus the quadrant and reference angle.
Unidade
Ângulo: 45° = 0,785398 rad
- 1
Convert to radians
45 × π ÷ 180 = 0,785398 - 2
Apply sine function
sin(0,785398 rad) = 0,707107
Como esta calculadora funciona?
For angle θ: sin and cos from the unit circle; tan = sin/cos; cot = cos/sin; sec = 1/cos; csc = 1/sin. Tan and sec are undefined at 90°+k·180°; cot and csc at k·180°. Enter θ in degrees or radians to get all six values, the quadrant, and the reference angle (acute angle to the x-axis).
Fórmula
How this is calculated
The six trigonometric functions define ratios between a right triangle's sides, generalised to all angles via the unit circle. For angle θ, the point (cos θ, sin θ) lies on the unit circle, giving the first two functions. The remaining four follow: tan θ = sin θ / cos θ, cot θ = cos θ / sin θ, sec θ = 1 / cos θ, csc θ = 1 / sin θ.
Tan and sec are undefined when cos θ = 0 (θ = 90° + k·180°); cot and csc are undefined when sin θ = 0 (θ = k·180°). The calculator detects these cases and displays "undefined". Small floating-point rounding errors near special angles (e.g., sin 180° ≈ 1.2×10⁻¹⁶ instead of 0) are clamped to zero when they fall below 10⁻¹⁰.
The reference angle is the acute angle (0°–90°) between the terminal side of θ and the nearest x-axis — useful for solving triangles by working with a first-quadrant equivalent and applying the quadrant sign rules: sin > 0 in Q I and Q II; cos > 0 in Q I and Q IV; tan > 0 in Q I and Q III.
Perguntas frequentes
tan θ = sin θ / cos θ. At θ = 90°, cos 90° = 0, so the ratio involves division by zero and is undefined. Geometrically, the tangent line at 90° on the unit circle is vertical and never intersects the x-axis.
The reference angle is the positive acute angle between the terminal side of θ and the x-axis. It lets you find trig values in any quadrant: compute them for the reference angle (always 0°–90°), then apply the correct sign based on the quadrant (sin positive in Q I & II; cos positive in Q I & IV; tan positive in Q I & III).
Radians = degrees × π/180; degrees = radians × 180/π. Key landmarks: 0° = 0, 30° = π/6, 45° = π/4, 60° = π/3, 90° = π/2, 180° = π, 270° = 3π/2, 360° = 2π.
Também conhecido como
TG we-Calculate Editorial Team. (2026). Theta (θ) Calculator — All Six Trigonometric Functions [Online calculator]. TG we-Calculate. https://we-calculate.com/pt/calculator/theta-calculator
TG we-Calculate Editorial Team. "Theta (θ) Calculator — All Six Trigonometric Functions." TG we-Calculate. 2026. https://we-calculate.com/pt/calculator/theta-calculator.
TG we-Calculate Editorial Team, "Theta (θ) Calculator — All Six Trigonometric Functions," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/pt/calculator/theta-calculator
@misc{wecalculate_theta_calculator, title = {Theta (θ) Calculator — All Six Trigonometric Functions}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/pt/calculator/theta-calculator}}, year = {2026}, note = {TG we-Calculate} }
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