Calculator with Cos and Sin

Trigonometric Functions:

\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \] \[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]

Result:

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1. What are Cosine and Sine?

Cosine (cos) and sine (sin) are fundamental trigonometric functions that relate the angles of a right triangle to the ratios of its sides. They are periodic functions with applications across mathematics, physics, engineering, and more.

2. How Does the Calculator Work?

The calculator uses PHP's built-in trigonometric functions:

\[ \cos(\theta) = \text{adjacent/hypotenuse} \] \[ \sin(\theta) = \text{opposite/hypotenuse} \]

Where:

\( \theta \) — Angle in degrees (0-360)
Values are dimensionless ratios
For example: cos(30°) = √3/2 ≈ 0.866025

Explanation: The calculator converts the angle from degrees to radians before applying the trigonometric function.

3. Importance of Trigonometric Functions

Details: Cosine and sine functions are essential in wave analysis, circular motion, alternating current circuits, sound waves, and many areas of physics and engineering.

4. Using the Calculator

Tips: Enter an angle between 0-360 degrees, select either cosine or sine function, and click calculate. The result will be a dimensionless ratio between -1 and 1.

5. Frequently Asked Questions (FAQ)

Q1: Why are the results between -1 and 1?
A: These functions represent ratios of triangle sides to hypotenuse, which can never exceed 1 in absolute value.

Q2: What's the difference between degrees and radians?
A: Degrees range 0-360 in a circle, while radians range 0-2π. The calculator handles the conversion automatically.

Q3: What are some key values to remember?
A: cos(0°)=1, cos(90°)=0, cos(180°)=-1, cos(270°)=0, and similarly for sine with phase shift.

Q4: Can I calculate inverse functions with this?
A: No, this calculator only computes cos and sin. For inverse functions (arccos, arcsin), you would need a different tool.

Q5: How accurate are the results?
A: The calculator uses PHP's built-in functions which are typically accurate to about 14 decimal places, though results are displayed to 6 decimal places.