Explanation
Powers, roots, logarithms and sine
Scientific operations answer questions that ordinary addition and division cannot. Roots reverse powers, logarithms reverse exponential growth, and sine relates an angle to a circular or right triangle proportion.
Choose a function
Choose one operation at a time. Integer powers accept exponents between −100 and 100. Square roots require a nonnegative value and natural logarithms require a positive value. Sine uses degrees; enter 90 for a right angle.
y = √x
| y | result |
|---|---|
| x | number entered |
y = xᵏ
| y | result |
|---|---|
| x | number entered |
| k | whole-number exponent |
y = ln x
| y | result |
|---|---|
| x | number entered |
y = sin(θ × π ÷ 180)
| y | result |
|---|---|
| θ | angle in degrees |
Square root of 9
| Number | 9 |
|---|---|
| Result | 3 |
√9 = 3
A negative integer power
| Base | 2 |
|---|---|
| Exponent (whole number) | -3 |
| Result | 0.125 |
2^-3 = 0.125
Natural log of 1
| Number | 1 |
|---|---|
| Result | 0 |
ln(1) = 0
A right angle
| Angle | 90 |
|---|---|
| Result | 1 |
sin(90°) = 1
Diagram of this result
The expression written out with its value.
The function, its input and the result are written as one expression. The exact numbers are stated in the answer and the steps.
Common mistakes
A negative exponent means a reciprocal, not a negative result: 2⁻³ = 1/8. The logarithm of zero has no finite value. Sine here takes degrees; convert radians first (multiply by 180 ÷ π). This calculator evaluates one function at a time; it does not parse whole expressions.
Assumptions and limits
The engine uses 50 significant digits. Roots, logarithms and trigonometry are approximate with absolute and relative fixture tolerance 1e−12. Sine angles are bounded to ±1,000,000 degrees and reduced modulo 360; exact quadrant angles return their exact signed values. Zero raised to zero or a negative exponent is rejected. Numeric observations use up to 30 significant input digits and 50 internal digits; no presentation rounding enters the calculation.
Sources
OpenStax Algebra and Trigonometry 2e: https://openstax.org/details/books/algebra-and-trigonometry-2e
Why is zero to the power zero rejected?
Different mathematical contexts use different conventions. This calculator treats the expression as undefined rather than choosing a convention silently.