Trigonometry Calculator Degree Mode

Basic Trigonometric Functions:

\[ \tan \theta = \frac{\sin \theta}{\cos \theta} \] \[ \sin^2 \theta + \cos^2 \theta = 1 \]

Result:

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1. What is Trigonometry?

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles. The primary trigonometric functions are sine (sin), cosine (cos), and tangent (tan).

2. Degree Mode Calculation

This calculator performs trigonometric calculations in degree mode (0° to 360°). The functions are calculated using these formulas:

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

3. Common Trigonometric Values

Important Values:

sin(0°) = 0, cos(0°) = 1, tan(0°) = 0
sin(30°) = 0.5, cos(30°) = √3/2 ≈ 0.866
sin(45°) = cos(45°) = √2/2 ≈ 0.707
tan(45°) = 1 (dimensionless)
sin(90°) = 1, cos(90°) = 0

4. Using the Calculator

Instructions: Enter an angle in degrees (0-360), select the trigonometric function, and click Calculate. The result will show the function value at that angle.

5. Frequently Asked Questions (FAQ)

Q1: Why does tan(90°) show an error?
A: Tangent is undefined at 90° because cos(90°) = 0, and division by zero is undefined.

Q2: What's the difference between degree and radian mode?
A: Degrees use 360° for a full circle, radians use 2π (about 6.283). This calculator uses degrees.

Q3: Are the results exact?
A: Results are approximations rounded to 6 decimal places, as exact values often involve irrational numbers.

Q4: Can I calculate inverse trigonometric functions?
A: This calculator only calculates standard trigonometric functions (sin, cos, tan) not their inverses.

Q5: What about angles beyond 360°?
A: Trigonometric functions are periodic (repeat every 360°), so 370° is equivalent to 10°.