Algebra Calculator Degrees

This algebra calculator handles degree-based measurements, including angle conversions, trigonometric functions, and polynomial solutions. Whether you're working with radians, degrees, or solving quadratic equations, this tool provides accurate results and explanations.

Introduction to Algebra with Degrees

Degrees are a fundamental unit of measurement in algebra, particularly when dealing with angles and trigonometry. This calculator helps you perform various algebraic operations involving degrees, from simple conversions to complex polynomial solutions.

Key concepts covered in this guide:

Angle conversions between degrees and radians
Trigonometric functions (sine, cosine, tangent)
Quadratic and cubic polynomial solutions

Degree Conversions

Degrees and radians are two common units for measuring angles. The conversion between them is straightforward:

Degrees to Radians: radians = degrees × (π/180)

Radians to Degrees: degrees = radians × (180/π)

For example, 90 degrees is equal to π/2 radians (approximately 1.5708 radians).

Degrees	Radians
0°	0
30°	π/6 ≈ 0.5236
45°	π/4 ≈ 0.7854
60°	π/3 ≈ 1.0472
90°	π/2 ≈ 1.5708

Trigonometric Functions

Trigonometric functions relate the angles of a triangle to the lengths of its sides. The primary functions are sine, cosine, and tangent:

Sine: sin(θ) = opposite/hypotenuse

Cosine: cos(θ) = adjacent/hypotenuse

Tangent: tan(θ) = opposite/adjacent = sin(θ)/cos(θ)

These functions are periodic and have specific values at standard angles:

Angle (degrees)	sin(θ)	cos(θ)	tan(θ)
0°	0	1	0
30°	0.5	√3/2 ≈ 0.8660	√3/3 ≈ 0.5774
45°	√2/2 ≈ 0.7071	√2/2 ≈ 0.7071	1
60°	√3/2 ≈ 0.8660	0.5	√3 ≈ 1.7321
90°	1	0	Undefined

Polynomial Solutions

Polynomial equations involve variables raised to whole number powers. The solutions to these equations are the values of the variable that satisfy the equation.

Quadratic Equation: ax² + bx + c = 0

Solutions: x = [-b ± √(b² - 4ac)] / (2a)

For example, solving 2x² - 5x + 2 = 0 gives two solutions:

x = [5 + √(25 - 16)] / 4 = [5 + 3]/4 = 2
x = [5 - √(25 - 16)] / 4 = [5 - 3]/4 = 0.5

Note: The discriminant (b² - 4ac) determines the nature of the roots:

Positive discriminant: Two distinct real roots
Zero discriminant: One real root (repeated)
Negative discriminant: Two complex roots

FAQ

What is the difference between degrees and radians?: Degrees and radians are both units for measuring angles, but they use different scales. A full circle is 360 degrees or 2π radians.
How do I convert degrees to radians?: Multiply the degree measurement by π/180 to convert to radians. For example, 90° × π/180 = π/2 radians.
What are the values of sine, cosine, and tangent at 45 degrees?: At 45 degrees, sin(45°) = cos(45°) = √2/2 ≈ 0.7071, and tan(45°) = 1.
How do I solve a quadratic equation?: Use the quadratic formula: x = [-b ± √(b² - 4ac)] / (2a). The discriminant (b² - 4ac) determines the number and type of solutions.
What is the difference between a polynomial and a trigonometric equation?: Polynomial equations involve variables raised to whole number powers, while trigonometric equations involve trigonometric functions of angles.