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Calculators

How to use a scientific calculator: angles, logs and factorials.

Degrees or radians, sin and its inverse, logs of any base, powers and roots, factorials and nCr on a scientific calculator, with exact answers where they exist.

By 5 min read

The sum 6 ÷ 2(1 + 2) drawn as six over two times one plus two, the answer 9, and a calculator keypad

A scientific calculator does what a school one does: powers, roots, logs, angles and counting. Here is how each works on KeepSimp's, and which answers it gives exactly.

Degrees or radians first.

Angles start in degrees, shown as DEG; press Deg to switch to radians. In degrees, sin 30 is exactly 0.5 and tan 45 is exactly 1; in radians, sin(π) is exactly 0 and cos(2π/3) is −0.5. The inverse keys give angles back in the unit in use: sin⁻¹(0.5) is 30 in degrees and π/6 in radians.

A common slip is sin(π) in degrees, which is the sine of π degrees. The calculator says so when you do it.

Powers, roots and logs.

xʸ raises to any power, x² squares, ʸ√x takes any root and 1/x turns a number over. Roots that come out even are exact: √(9/4) is 1.5 and the cube root of −27 is −3.

log is base 10 and ln is base e. For another base write log_2(8) or log₂8, which gives exactly 3. Logs that come out as simple fractions are found exactly, so log_8(2) is a third.

Factorials, nCr and nPr.

x! gives a factorial written in full, up to 10,000!. For a decimal such as 0.5! it uses the gamma function, worked out to 60 digits. 5 nCr 2 counts the ways to choose 2 of 5 when order does not matter (10), and 5 nPr 2 when it does (20).

Ans uses the last answer and the M keys keep a number in the memory. Every answer goes on the tape, which you can keep on your device if you choose.

Further reading

Topics: scientific calculator · how to use a scientific calculator · degrees or radians · log calculator · factorial calculator · ncr calculator

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