Theta Calculator
Calculate trigonometric functions, inverse functions, and double angle formulas for any angle θ
Calculate with Theta (θ)
Enter angle value
Choose angle unit
Trigonometric Functions
Calculation Details
Input: θ = 0° (0.000000 rad)
Special angle: 0°
Fundamental identity: sin²(θ) + cos²(θ) = 1.000000
Example: θ = 30°
Special Angle Values
sin(30°) = 1/2 = 0.5
cos(30°) = √3/2 ≈ 0.866
tan(30°) = 1/√3 ≈ 0.577
Step-by-step Calculation
Step 1: Convert to radians: 30° = π/6 ≈ 0.5236 rad
Step 2: Calculate sin(30°) = 0.5
Step 3: Calculate cos(30°) using identity: cos²(30°) = 1 - sin²(30°) = 1 - 0.25 = 0.75
Step 4: Therefore cos(30°) = √0.75 = √3/2 ≈ 0.866
Step 5: Calculate tan(30°) = sin(30°)/cos(30°) = 0.5/0.866 ≈ 0.577
Special Angles
Key Formulas
Fundamental Identity
sin²(θ) + cos²(θ) = 1
Tangent Ratio
tan(θ) = sin(θ) / cos(θ)
Reciprocal Functions
csc(θ) = 1/sin(θ)
sec(θ) = 1/cos(θ)
cot(θ) = 1/tan(θ)
Quick Tips
θ (theta) represents any angle
Convert: degrees = radians × 180/π
sin²(θ) + cos²(θ) always equals 1
Special angles have exact values
Use inverse functions to find angles
Understanding Theta (θ) in Trigonometry
What is Theta?
Theta (θ) is a Greek letter commonly used to represent angles in mathematics and physics. When you see θ in a mathematical context, it typically refers to an angle measurement.
θ = angle (in degrees or radians)
Trigonometric Functions
- •Sine (sin): Vertical component on unit circle
- •Cosine (cos): Horizontal component on unit circle
- •Tangent (tan): Ratio of sine to cosine
Applications
- •Physics: Wave functions, oscillations, rotational motion
- •Engineering: Signal processing, electrical circuits
- •Navigation: GPS systems, astronomy, surveying
- •Computer Graphics: 3D rotations, animations
Double Angle Formulas
sin(2θ) = 2sin(θ)cos(θ)
cos(2θ) = cos²(θ) - sin²(θ)
tan(2θ) = 2tan(θ)/(1-tan²(θ))