Free Online Trigonometry Calculator

📐 Free Online Trigonometry Calculator 🧮

This free online trigonometry calculator can help you compute values for trigonometric functions such as sine, cosine, tangent, cotangent, secant, and cosecant, given an angle in degrees or radians. It's designed to simplify your calculations and provide accurate results quickly.

✍️ How to Use the Calculator

1. Enter the Angle: Input the angle value in either degrees or radians.
2. Select the Unit: Choose whether the angle is in degrees or radians.
3. Compute: Click the calculate button to find the values for all six trigonometric functions.

🧮 Trigonometric Functions Explained

• Sine (sin): The ratio of the length of the opposite side to the length of the hypotenuse in a right triangle.
• Cosine (cos): The ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle.
• Tangent (tan): The ratio of the length of the opposite side to the length of the adjacent side in a right triangle. It can also be expressed as $tan(x) = \frac{sin(x)}{cos(x)}$.
• Cotangent (cot): The reciprocal of the tangent function. $cot(x) = \frac{1}{tan(x)} = \frac{cos(x)}{sin(x)}$.
• Secant (sec): The reciprocal of the cosine function. $sec(x) = \frac{1}{cos(x)}$.
• Cosecant (csc): The reciprocal of the sine function. $csc(x) = \frac{1}{sin(x)}$.

💻 Example Calculation

Let's calculate the trigonometric functions for 30 degrees:

import math

angle_degrees = 30
angle_radians = math.radians(angle_degrees)

sin_value = math.sin(angle_radians)
cos_value = math.cos(angle_radians)
tan_value = math.tan(angle_radians)
cot_value = 1 / tan_value
sec_value = 1 / cos_value
csc_value = 1 / sin_value

print(f"Sine: {sin_value}")
print(f"Cosine: {cos_value}")
print(f"Tangent: {tan_value}")
print(f"Cotangent: {cot_value}")
print(f"Secant: {sec_value}")
print(f"Cosecant: {csc_value}")

Output:

Sine: 0.49999999999999994
Cosine: 0.8660254037844387
Tangent: 0.5773502691896257
Cotangent: 1.7320508075688772
Secant: 1.1547005383792517
Cosecant: 2.0000000000000004

🔑 Key Trigonometric Identities

• Pythagorean Identity: $sin^2(x) + cos^2(x) = 1$
• Tangent Identity: $tan(x) = \frac{sin(x)}{cos(x)}$
• Cotangent Identity: $cot(x) = \frac{cos(x)}{sin(x)}$

💡 Why Use This Calculator?

• Accuracy: Provides precise calculations for all trigonometric functions.
• Efficiency: Saves time by quickly computing values.
• Accessibility: Available online, accessible from any device.