Trig Calculator
Calculate trigonometric functions and solve right triangle problems
Calculator Mode
Calculate Trigonometric Functions
Enter the angle to calculate all trigonometric functions
Trigonometric Functions
Unit Circle Reference
Common Angles (degrees):
0° → sin = 0, cos = 1
30° → sin = 1/2, cos = √3/2
45° → sin = √2/2, cos = √2/2
60° → sin = √3/2, cos = 1/2
90° → sin = 1, cos = 0
180° → sin = 0, cos = -1
270° → sin = -1, cos = 0
Key Identities
Reciprocal Identities:
csc(θ) = 1/sin(θ)
sec(θ) = 1/cos(θ)
cot(θ) = 1/tan(θ)
Quotient Identities:
tan(θ) = sin(θ)/cos(θ)
cot(θ) = cos(θ)/sin(θ)
Pythagorean Identity:
sin²(θ) + cos²(θ) = 1
Quick Tips
Remember SOHCAHTOA for right triangles
Sine and cosine values range from -1 to 1
Tangent is undefined at 90°, 270°, etc.
Functions repeat every 360° (2π radians)
Understanding Trigonometric Functions
What are Trigonometric Functions?
Trigonometric functions are mathematical functions that relate the angles of a triangle to the ratios of its sides. They are fundamental in mathematics, physics, engineering, and many other fields.
The Six Basic Functions:
- •Sine (sin): Opposite side ÷ Hypotenuse
- •Cosine (cos): Adjacent side ÷ Hypotenuse
- •Tangent (tan): Opposite side ÷ Adjacent side
- •Cosecant (csc): 1 ÷ sin(θ)
- •Secant (sec): 1 ÷ cos(θ)
- •Cotangent (cot): 1 ÷ tan(θ)
Applications
- •Engineering and construction calculations
- •Physics and wave analysis
- •Navigation and GPS systems
- •Computer graphics and game development
- •Signal processing and electronics
SOHCAHTOA Mnemonic:
SOH-CAH-TOA
Sine = Opposite ÷ Hypotenuse
Cosine = Adjacent ÷ Hypotenuse
Tangent = Opposite ÷ Adjacent