Trigonometry Calculator
Trigonometric functions (sin, cos, tan, csc, sec, cot) relate the angles and sides of triangles. They extend to the unit circle for all angles and are fundamental in physics, engineering, navigation, signal processing, and wave analysis.
💡
Tip: Remember CAST (All Students Take Calculus) for which functions are positive in each quadrant: Q1=All, Q2=Sin, Q3=Tan, Q4=Cos.
- 1In a right triangle: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent
- 2Mnemonic: SOH-CAH-TOA
- 3Unit circle definition: sin θ = y-coordinate, cos θ = x-coordinate, at angle θ from positive x-axis
- 4Reciprocals: csc = 1/sin, sec = 1/cos, cot = 1/tan
sin 30°=0.5sin(π/6) = 1/2
cos 60°=0.5cos(π/3) = 1/2
tan 45°=1tan(π/4) = sin/cos = 1
| Angle | sin | cos | tan |
|---|---|---|---|
| 0° (0) | 0 | 1 | 0 |
| 30° (π/6) | 1/2 | √3/2 | 1/√3 |
| 45° (π/4) | √2/2 | √2/2 | 1 |
| 60° (π/3) | √3/2 | 1/2 | √3 |
| 90° (π/2) | 1 | 0 | Undefined |
| 180° (π) | 0 | −1 | 0 |
⭐
Fun Fact
Jean Baptiste Joseph Fourier (1768–1830) showed that any periodic signal — no matter how complex — can be decomposed into a sum of sine and cosine waves. This Fourier transform is fundamental to audio compression (MP3), image compression (JPEG), and telecommunications.
References
🔒
୧୦୦% ମାଗଣା
ପଞ୍ଜୀକରଣ ଆବଶ୍ୟକ ନାହିଁ
✓
ସଠିକ
ଯାଞ୍ଚ ହୋଇଥିବା ସୂତ୍ର
⚡
ତତ୍କ୍ଷଣ
ତତ୍କ୍ଷଣ ଫଳ
📱
ମୋବାଇଲ୍ ଅନୁକୂଳ
ସମସ୍ତ ଡିଭାଇସ୍