Scientific calculator and graphing calculator

Brackets first, then functions such as sin or √ and the signs written after a number (!, %, ², ⁻¹). Powers come next and are read from right to left: 2^3^2 = 2^9 = 512. A leading minus applies after the power, so −2² = −4 while (−2)² = 4. Then × and ÷ from left to right, then + and −. A number written next to a bracket or π, as in 2π, is multiplied like ×, so 6 ÷ 2π means (6 ÷ 2)·π; write 6 ÷ (2π) for the other reading. % divides by 100: 50% = 0.5.

They are two units for angles: a full turn is 360 degrees or 2π radians, so 180° = π rad. In DEG mode sin 30 = 0.5; in RAD mode the same keys give the sine of 30 radians, about −0.988. The switch also sets the unit of the answers of sin⁻¹, cos⁻¹ and tan⁻¹. In the Graphs tab x is always in radians.

x² squares what stands before it, and with 2nd it becomes x³. For any other power use ^: 2^10 = 1024, 2^−1 = 0.5. √ takes the square root of what follows: √16 = 4, √(9 + 16) = 5. Other roots are fractional powers: the cube root of 27 is 27^(1/3) = 3. A negative number under a fractional power, such as (−8)^(1/3), is reported as outside the domain; write −(8^(1/3)) instead. In the Graphs tab cbrt(x) draws the cube root for negative x too.

Numerically, inside the part of the plane you see. The visible x-range is split into 2,000 equal steps; where f(x) changes sign between two steps, that interval is halved 80 times (bisection), and a sign change at a vertical asymptote, as for 1/x at 0, is rejected. Minima and maxima are where the numerical derivative changes sign, and a root where the graph only touches the axis, like x² at 0, is found as such a point with y = 0. Intersections are the roots of f − g. Two roots closer than one step can be missed, so zoom in to check.