Trig Calculator Sin Cos Tan

Trigonometric Functions:

\[ \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)} \]

Result:

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1. What are Trigonometric Functions?

Trigonometric functions (sine, cosine, tangent) relate angles of a right triangle to ratios of its sides. They are fundamental in mathematics, physics, engineering, and many other fields.

2. How Does the Calculator Work?

The calculator uses the basic trigonometric relationships:

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

Where:

\( \theta \) — Angle in degrees
All trigonometric functions are dimensionless
Calculations are performed using radians internally

Explanation: The calculator converts your angle from degrees to radians, then computes the selected trigonometric function.

3. Importance of Trigonometry

Details: Trigonometric functions are essential for solving problems involving triangles, waves, oscillations, and circular motion. They appear in physics, engineering, computer graphics, and more.

4. Using the Calculator

Tips: Enter an angle in degrees (0-360 for best results) and select which trigonometric function you want to calculate. The result will be a dimensionless ratio.

5. Frequently Asked Questions (FAQ)

Q1: Why is my tangent result so large?
A: Tangent approaches infinity as the angle approaches 90° (or 270°). For angles near these values, you'll get very large results.

Q2: What's the range of sine and cosine?
A: Both sine and cosine return values between -1 and 1 for all real angles.

Q3: Can I calculate inverse trigonometric functions?
A: This calculator only computes standard trigonometric functions. Inverse functions would require a different calculator.

Q4: Why convert degrees to radians?
A: Programming languages typically use radians for trigonometric calculations, so we convert your degree input for accurate results.

Q5: What about other trig functions like secant or cosecant?
A: These can be calculated as reciprocals of the basic functions (sec = 1/cos, csc = 1/sin, cot = 1/tan).