Trig Degree Calculator
Calculate trigonometric functions for angles in degrees with exact values
Calculate Trigonometric Functions in Degrees
Enter any angle in degrees to calculate all trigonometric functions
Trigonometric Functions for 30°
Quadrant: I (sin > 0, cos > 0)
Reference Angle: 30°
Coterminal Angle (0-360°): 30°
Special Angle Values
Quadrant I (0° - 90°):
0°: sin=0, cos=1, tan=0
30°: sin=1/2, cos=√3/2, tan=1/√3
45°: sin=√2/2, cos=√2/2, tan=1
60°: sin=√3/2, cos=1/2, tan=√3
90°: sin=1, cos=0, tan=undefined
Quadrant II (90° - 180°):
120°: sin=√3/2, cos=-1/2
135°: sin=√2/2, cos=-√2/2
150°: sin=1/2, cos=-√3/2
180°: sin=0, cos=-1
Function Signs by Quadrant
Quadrant I (0° - 90°):
All positive: sin+, cos+, tan+
Quadrant II (90° - 180°):
sin+, cos-, tan-, cot-
Quadrant III (180° - 270°):
sin-, cos-, tan+, cot+
Quadrant IV (270° - 360°):
sin-, cos+, tan-, cot-
Quick Tips
Use exact values for precise mathematical work
Remember: 30-60-90 and 45-45-90 special triangles
Functions repeat every 360° (full circle)
Use reference angles to find values in any quadrant
Understanding Trigonometric Functions in Degrees
Degree Mode vs. Radian Mode
Degrees are more intuitive for many people since a full circle is 360°. This calculator focuses specifically on degree measurements, making it perfect for geometry, navigation, and everyday applications.
Exact vs. Decimal Values
- •Exact values: Use fractions and radicals for precise calculations
- •Decimal values: Use for approximate calculations and comparisons
- •Special angles: 0°, 30°, 45°, 60°, 90° have exact values
Trigonometric Identities
Basic Identities:
tan(θ) = sin(θ)/cos(θ)
cot(θ) = cos(θ)/sin(θ) = 1/tan(θ)
sec(θ) = 1/cos(θ)
csc(θ) = 1/sin(θ)
sin²(θ) + cos²(θ) = 1
Applications
- •Navigation and compass bearings
- •Geometry and triangle problems
- •Engineering and construction
- •Physics and wave analysis
Common Angle Reference Chart
| Angle | sin | cos | tan | csc | sec | cot |
|---|---|---|---|---|---|---|
| 0° | 0 | 1 | 0 | undefined | 1 | undefined |
| 30° | 1/2 | √3/2 | 1/√3 | 2 | 2/√3 | √3 |
| 45° | √2/2 | √2/2 | 1 | √2 | √2 | 1 |
| 60° | √3/2 | 1/2 | √3 | 2/√3 | 2 | 1/√3 |
| 90° | 1 | 0 | undefined | 1 | undefined | 0 |
| 120° | √3/2 | -1/2 | -√3 | 2/√3 | -2 | -1/√3 |
| 135° | √2/2 | -√2/2 | -1 | √2 | -√2 | -1 |
| 150° | 1/2 | -√3/2 | -1/√3 | 2 | -2/√3 | -√3 |
| 180° | 0 | -1 | 0 | undefined | -1 | undefined |